What are the coordinates of the triangle after a dilation with a scale factor of 2? center it at (2, 2) .

Dilation of a point P(x,y) with scale factor s centred at (p,q) is given by
P'=(p+s*(x-p),q+s*(x-q))

Substituting 
s=2, p=2,q=2
P'=(2+2*(x-2),2+2*(y-2))

P           P'
(2,4)      (2+2(2-2), 2+2*(4-2)) = (2, 6)
(0,6)      (2+2(0-2), 2+2*(6-2)) = (-2, 10)
(-3,3)     (2+2(-3-2), 2+2*(3-2)) = (-8, 4)

The coordinates are (-8, 4), (-2, 10), (2, 6).

Each point has moved twice as far away from (2, 2) as it was originally. Each coordinate (x, y) becomes (2x-2, 2y-2).