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The analyzer has me (white) up here by 4.88. It's telling me my best move is d4. But, I don't know why that move is good. Any ideas?
It speeds up the development of your bishop, and protects your knight.
You're up a piece. That game is over, unless you blunder. Qe2 probably works as well.
P.S., you only need +1.5 for a winning game.
oh boy...I missed the Q protects the pawn...
More to the point, only one other move (Qh5) even comes close to defending your Knight (which can't move, or the Bishop will be left hanging) and this fails quickly to d6 after which either the Knight or the Bishop will fall, not to mention the precarious position it puts your Queen in so early in the game. d4 not only protects the Knight, but also interposes on the Queen's attack on your Bishop should the Knight be driven away.
There is also the threat of Bxh6 followed by grabbing a pawn on f7.