This question is a bit problematic because -2/3x can be understood as (-2/3) * (X) or (-2) / (3X)
But since the question is about coefficient, then it should pose no problem to solve it. Assuming the question mean (-2/3) * (X), then
(-2/3) * (X) * 3Y * (-2X) =
(-2/3 * 3*-2) * X^2 * Y =
(4) * X^2 * Y
That means the coefficient will be 4