For those who want visual clarification on the position...
The typical Vancura position does indeed have the king further back than in this position. This is probably the most complicated variation of the Vancura, and it's strange that chess.com would put this as the drill without first putting the regular idea that players usually do. The idea is that white would like to check the black king along the 8th rank, and then use that tempo to drop his rook down to the 3rd rank where it can attack the pawn from the side, and from there its a draw. Here, black has the tactical resource of going Kd4, and if white tries to get his rook to the third rank with Rc3 as per usual, black can play Rb1+, sacrificing the rook, so that they can then pick up white's rook when the king leaves it undefended. If White attempts to save the rook with Kc2, black can follow up with Rc1+, skewering the king and forcing the trade.
Something similar to this Vancura position occurred in the game Radjabov v. Nakamrua in the Vugar Gashimov Memorial Tournament in 2014, and Nakamura achieved a draw. The moves leading up were different to the drill on chess.com, but it transposes after white's first move. I'll demonstrate how he achieved the draw through this position, and I recommend looking at the game if you get a chance.
You are correct in saying that you'll want to abandon the idea of reaching the third rank via a tempo check. Instead, you'll want to play the move Rh4. The best response for black is to play Kd5 (if he moves to the sixth rank, you'll just check him from the fourth rank, then put your rook on the third rank and achieve the regular defense from before. If he plays Rh2+, put a hold on what to do for right now, because it will become clear after you study the positions below). After Kd5, you can play the move Rg4 (Rf4 also draws). Black can respond in a number of ways.
- If any random king move: White will play Rg3, and you've achieved the regular Vancura position.
- If black marches with h2: White will play the rook back via Rh4, and then Rh8 and influence the pawn from behind. The black rook can never leave h1, because then white will pick off the pawn, and as soon as black's king gets close to the pawn, White can check it with tempo from the 8th rank, driving it away, and then return to the h file.
And now the more complicated variations:
- If the rook moves along the 1st rank via Rf1/Re1/Rd1, white will retreat back with Rh4. Black will play Rf3 to protect the pawn (Rh1, Rg4 repeats), and then white's king is free to head towards the h pawn without having to fear losing control of the a2 square and falling for a skewer. Here's how such a variation might look:
- (Note: if he plays Rf1, after Rh4, he could also play Rf2+, and then h2, but if so, just play Kc3 and see the idea above). One thing to be aware of, if black does play Ra2 at any point, don't play Rxh3, because black will have the tactic Ra3+. Instead, keep marching your king towards the pawn, and if Black's king gets to your rook, put your rook on h8)
- And finally, black's response that demands the most technique from the defender is Rh2+. This leads to a critical position in which White only has one winning move. White must respond with the accurate move Kb3!, in order to maintain control of the a2 square for just a little longer and still prevent possible skewers. All other moves are losing (see side variations below).
If black decides to then play Rf2/Re2/Rd2, we have the same idea from above, by putting our rook on h4, forcing Rf3+/Re3+/Rd3+ or a repeating position, and then after moving our king forward on the second rank, we can bring the king forward to attack the pawn. Variations play out the same as above, with more tempo for white the closer black placed their rook to our king.
Black could also try Rg2, but it plays out the same as above. Rh4, Rg3+ or repeating, Kc2, and it will be a draw.
If black plays any king move, we will place our rook on g3, and achieve a regular Vancura idea of controlling the pawn from the side. This will be a draw. In the game with Nakamura, Radjabov attempted the equivalent, in our position, of Kd4, but white simply played Rf3. If ever Rh1, White responds with Kb2, and it is a clear draw.
Hope this all helped!
I learned the Vancura position pretty well, from more than 4-5 sources (including practicing on chessable).
But on chess.com drills (https://www.chess.com/drills/practice/rook-endgame-the-vancura-position) IF the black king goes to d4 than it's all hopeless, because Black will get the Rook out on the 1st rank (unless the computer does not do this). I don't know where I saw / read that in that possition I should not check at c8, but bring my Rook to f3 and then down on the 3rd rank, but Black can just get the Rook out and it's game over. If I start by going down on the h file (h4) then the King starts moving and I am down one tempo and I will not be able to get into the checking position or on the 3rd rank as the Black will get the Rook out.
How can you draw with the opponent King in that possition? (all other sources start with the King farther away).