Since on step 1 you have $\
eg \forall y P(x,y)$, you get $\exists y \
eg P(x,y)$, and thus you end up with $\exists d$ rather than $\forall d$ on line 2.
Also, I would move this $\exists d$ right after the $\exists a$, otherwise you would need to use functions when doing skolemization, and fortunately you can do that by first bringing out the $a$ and $d$ using the Prenex laws before bringing out the $b$ and $c$. (Also, if you get graded on your work, I would show all those steps)
And so on the last step you just need a constant instead of the $d$ (And of course you get rid of that quantifier)