$\begin{aligned} & 2 P(x=3)=3 p(x=2) \\ & \Rightarrow 2 \times{ }^4 c_3(1-q)^3 q=3 \times{ }^4 c_2(1-q)^2 q^2 \\ & \Rightarrow 2 \times 4 \times(1-q)=3 \times 6 \times q \\ & \Rightarrow \frac{4}{9}=\frac{q}{1-q} \\ & \Rightarrow q=\frac{4}{13}\end{aligned}$