Your computer will tell you what it is thinking. The first thing it says is that black already has an advantage. I ran it on my Stockfish 7 and the move 6 h3 never appeared in the list of top moves.
What computer are you running?
At any rate, a computer doesn't just give moves. Normally, it gives you multiple lines that it is working on and it tells you how far out it is looking. You can have the computer focus on one line or work on multiple lines. (Of course, there is a trade-off when you start considering multiple lines.)
What lines is it giving with 6 h3? (You don't need to post 20 moves. Just a few half moves will show what it was thinking.)
I assume it also gave you 5 Ng5, right? That doesn't make any sense either. Stockfish says that taking that move back (moving the knight back to f3) would be one of your best choices.
In this dragon position, my computer has suggested the move 6.h3
I've looked at the position for long enough. I don't understand the reason for the move. There must be some meaning behind it. My computer actually hung onto it for a long time as the best move but was eventually bumped down by 6.Nc3, which I do understand.
6.h3 though? I don't get it. Why is that a good move?
I run into this kind of stuff all the time with my computer. It suggests moves and I have no idea why. Not understanding moves like this is part of the reason why I'm not getting any better.
Anybody got a good explanation for 6.h3?