Rewrite the given equation yields $$ax-2 = 3(x-2) \implies (a-3)x + 4=0$$

This equation will have no solution when the coefficient of the $x$ term equals $0$. Hence, $a=3$ is one solution.

In addition, the original equation implies $x\ne 2$. Setting $x=2$ to the above relation leads to $a=1$.

Hence, there are two answers to the original question: $a=1$ or $a=3$.