Y^2+4x-6x-6y+5=0
convert to standard form, find the vertex, focus, and the equation of the directrix line

I think it is :.

But...not really sure

So first we group like terms
y^2+4x-6x-6y+5=0
y^2-6y-2x+5=0
so I suspect that you might have left out a x^2 but I'll try to solve it how it is

y^2-6y+5-2x=0
factor y^2-6y+5
what adds up to -6 and multiplies to get 5, -1 and -5
(y-5)(y-1)-2x=0
not sure how to procede but you could get it to this
(y-5)(y-1)=2x