First, I'd like to point out that the question should really read:

"If a certain triangle T has vertices at the points (0,0) and (6,0) and centre at the point (3,2)...", because without the "certain triangle T" part the third vertex could be any point in the xy plane (i.e. the question never explicitly says that the triangle follows the T rule, although we know it must, otherwise there'd be no answer to the question).

We know that the x-co-ordinate of the centre is the average of the 3 x-co-ordinates. So:

avg = sum/# of terms
3 = (0 + 6 + x)/3
9 = 6 + x
3 = x

We also know that the y-co-ordinate of the centre is the average of the 3 y-co-ordinates. So:

2 = (0 + 0 + Y)/3
6 = y

Therefore our missing co-ordinate is (3,6): choose (B).