Since our charge is located at (a,a) the image charge to make the bottom plane
arounded is loacted at a point (a,a)

WRONG... the charge is located at (a/2, sqrt(3)/2) as in the figure... and the image charge
is (a/2, sqrt(3)/2)...
Now for hte plane at 60 degrees. the image charge has to be located a distance a/2 from the plate but at an angle.

Yup.. you are correct...
Is it safe to assume that this point is going to be on the Y axis?? such that it turns into the placement like in the diagram??

WRONG... the image charge is not on the Y axis....
Finding the coordiantes of this point is what is troubling me.

Then hard work on it...
i think to neutralize the potnetial at the origin im goig to need three more charge located diametrically opoosite location. So in the end we will have 6 charges?? I am currently working on it.

Yes, you will end up with 6 charges (including the original one)...
GOOD LUCK