smc

We know that $2^{6x+3}\cdot 4^{3x+6}=2^{6x+3}\cdot (2^2{)}^{3x+6}=2^{6x+3}\cdot 2^{6x+12}=2^{12x+15}$. We also know that $8^{4x+5}=(2^3{)}^{4x+5}=2^{12x+15}$. There are infinite solutions to the equation $2^{12x+15}=2^{12x+15}$, so the answer is $\boxed{\text{greater than 3}}$.