Answer
By the binomial theorem, we have
$(2x+(-3y))^{200}=\sum {200\choose j}(2x)^{200-y}(-3y)^j$
Consequently, the coefficient of $x^{101}y^{99}$ in the expansion is obtained when $j =99$ is,
$${200\choose 99}2^{101}(-3)^{99}=-\frac{200!}{99!101!}2^{101}3^{99}$$
Work Step by Step
As given above