For starters, Black is best off not taking the pawn. I assume you mean 4.Nc3, against which 4...d6 scores really well for Black rather than 4...Qxb2.
London System early c5-line
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Basically, to open the diagonal for the DSB and attack on the queenside with rook/knight/bishop after playing c4.
Many times (in 1.d4 games) an issue for White is where the DSB belongs. Usually, it isn't d2, and sometimes c1 is the place to be for a while.
Qb6 tries to prove this point.
Another ongoing thread (somewhat related)
https://www.chess.com/forum/view/chess-openings/what-to-play-against-the-old-benoni
4.Nc3 is the only good move after 3...Qb6. I do not like 4.Na3 because of the simple 4...cxd4 5.exd4 Nd5! when the only good move for white is 6.Bc1 which gives Black a very comfortable game after, say, 6...g6.
Now 4...Qxb2 is not worth the risk (white has a draw at hand after 5.Nb5, and maybe more than that), 4...d6 followed by ...e5 is solid and fine, but I prefer the more active 4...e6 with complicated play. I have won a game recently playing like that as Black, but it's not worth showing it as white played very poorly.
Sorry for confusing post. I left out a some moves. In the image attached we've reached there by the following moves:
1.d4 Nf6 2. Bf4 c5 3. e3 Qb6 4. Nc3 Qxb2 5. Nb5 Nd5 6. a3 a6 7. Rb1 Qa2 8. Qc1 axb5 9. Ra1 Qxa1 10. Qxa1 e5. It's the 10... e5 move I don't understand. It gives white a pawn.
herr_shaibel wrote:
Sorry for confusing post. I left out a some moves. In the image attached we've reached there by the following moves:
1.d4 Nf6 2. Bf4 c5 3. e3 Qb6 4. Nc3 Qxb2 5. Nb5 Nd5 6. a3 a6 7. Rb1 Qa2 8. Qc1 axb5 9. Ra1 Qxa1 10. Qxa1 e5. It's the 10... e5 move I don't understand. It gives white a pawn.
I'm with pfren on not take the pawn after 4.Nc3, but with 4.Na3 and I'd fulfill the threat and look to draw by the simpler means. At higher levels, you might look to complicate things (looking for a win) and follow up with 6...e6 (after the line he gave with 4...cxd4)
Here is the whole episode "London System against an early c5": https://youtu.be/N9CczxstD2g I do understand that black should never go Qxb2. It's the 10... e5 that seems unnecessary.
#8
10...e5 is to open the diagonal of Bf8 and to prepare ...O-O
Black should take 4...Qxb2 the poisoned pawn on b2, otherwise 3...Qb6 has no point.
tygxc wrote:
#8
10...e5 is to open the diagonal of Bf8 and to prepare ...O-O
Black should take 4...Qxb2 the poisoned pawn on b2, otherwise 3...Qb6 has no point.
The other point was cxd4
Edit: video referenced (12:00 ish)
PerpetuallyPinned wrote:
I'm with pfren on not take the pawn after 4.Nc3, but with 4.Na3 and I'd fulfill the threat and look to draw by the simpler means. At higher levels, you might look to complicate things (looking for a win) and follow up with 6...e6 (after the line he gave with 4...cxd4)
...Qb6 is played to force a concession by white, and also to put some pressure against the d4 pawn. Black should not take at b2 after 4.na3 too, as 4.Na3 Qxb2 5.Nb5 transposes to the Nc3 line.
herr_shaibel wrote:
Sorry for confusing post. I left out a some moves. In the image attached we've reached there by the following moves:
1.d4 Nf6 2. Bf4 c5 3. e3 Qb6 4. Nc3 Qxb2 5. Nb5 Nd5 6. a3 a6 7. Rb1 Qa2 8. Qc1 axb5 9. Ra1 Qxa1 10. Qxa1 e5. It's the 10... e5 move I don't understand. It gives white a pawn.
Black should do something very quickly before white is able to stabilize his position.
10...e5! is practically forced, and it's based on a not-so-subtle tactic: after 11.Bxe5 c4! Black is just in time to attack the white king with moves like ...Bb4+, and of course annoy the white queen since the a3 pawn is hanging.
tygxc wrote:
#8
10...e5 is to open the diagonal of Bf8 and to prepare ...O-O
Black should take 4...Qxb2 the poisoned pawn on b2, otherwise 3...Qb6 has no point.
No, 10...e5! is definitely not played to prepare castling. Far from it.
And about taking the b2 pawn: Ever heard of a patzer named Aron Nimzowitz, who claimed that the threat is stronger than the execution?
4...Qxb2 is not a move Black should play, first because it forces Black to play several "only moves" in the process to stay alive, and second because it allows "games" like the following one:
pfren, thanks, I understand now. Black need to create havoc as long as the king is exposed and white is undeveloped on the kingside. On the other hand black has some pieces hanging, attacked by the queen and the dark-squared bishop.
pfren wrote:
tygxc wrote:
#8
10...e5 is to open the diagonal of Bf8 and to prepare ...O-O
Black should take 4...Qxb2 the poisoned pawn on b2, otherwise 3...Qb6 has no point.
No, 10...e5! is definitely not played to prepare castling. Far from it.
An about taking the b2 pawn: Ever heard of a patzer named Aron Nimzowitz, who claimed that the threat is stronger than the execution?
4...Qxb2 is not a move Black should play, first because it forces Black to play several "only moves" in the process to stay alive, and second because it allows "games" like the following one:
Even faster than the famous Berlin draw. 
herr_shaibel wrote:
pfren, thanks, I understand now. Black need to create havoc as long as the king is exposed and white is undeveloped on the kingside. On the other hand black has some pieces hanging, attacked by the queen and the dark-squared bishop.
Quite right. Also, it's remarkable that after 10...e5! white should rather take with the pawn there, again for a very concrete reason: this gives the white queen a safe escape square at d4.
Like for example in the following high level ICCF game, which resulted in a small chaos, and eventually a draw- something very common in computer-aided games.
Wow, the white queen does everything there.
herr_shaibel wrote:
pfren, thanks, I understand now. Black need to create havoc as long as the king is exposed and white is undeveloped on the kingside. On the other hand black has some pieces hanging, attacked by the queen and the dark-squared bishop.
He's showing you how to fight for winning chances.
I (and Hanging Pawns) was showing how to draw with Black playing after the queen exchange (I thought). The video was for White (London System vs Benoni set up and playing e3). The game pfren posted (#18) is interesting (16.g4 I never considered) and a deep analysis would be nice (if only that game were annotated).
I also sort overlooked the safe square (d4) for White's queen. I focused on the route of 11...Nxf4 12.exf4 c4
I'm sure it's very difficult either way. But perhaps for both sides at lower levels (not just Black).
Thanks @pfren for sharing valuable and concrete insights/games
This is a theorethical line starting with 1. d4 Nf6 2. Bf4 c5 3. e3 Qb6. Black is attacking the b2 pawn but has to give up the queen for a knight and a rook. After that black should play e5, and I really don't get why send out the pawn unprotected like this (from Hanging Pawns). Any thoughts?