I know that the answer is (4, 16, 2) but not sure how to get this, please explain!!
3 Answers

Well, you didn’t provide possible answers, so I’m just going to assume all the other ones are obviously wrong and focus on why (4,16,2) is right.
if you plug in (x=4, y=16, z=2) to the plane equation:
3(4) – 2(16) + 4(2) = 12 – 32 + 8 = 12
Since 12 = 12, this point is on the plane.

Any point lying in the plane must have coordinates such that they satisfy the equation of the plane. Except for having three coordinates, it’s just the same as confirming a point is on a line
3x – 2y + 4z = 12 …Insert the x,y,z values
12 – 32 + 8 = 12.
QED

possible answers
a (2,–2, 3)
b (5, 15, 2)
c (4, 16, 2) < this one
d (–4, 3,–2)