Question

write an equation for a circle with center at (6,-2) and diameter = 12

Answer 1

Diameter is just twice the radius, which is what you really need :D
If you want a circle with its center at a point (h, k) and a radius r, then its equation is given by
\[\large (x-h)^2 + (y-k)^2 = r^2\]

Answer 2

so in this situation, your diameter, which is twice your radius, is 12, meaning your radius r is just half of that.

And your center (h, k) is at (6 , -2)
implying h = 6 and k = -2

Plug in :)