Find the derivative $f^{\prime }(x)$: $f^{\prime }(x)=6x^2-18ax+12a^2$ $f^{\prime }(x)=6(x^2-3ax+2a^2)=6(x-a)(x-2a)$.

Identify critical points: The critical points are $x=a$ and $x=2a$. Since $a>0$, we have $a<2a$.

Determine Max/Min: The leading coefficient is positive, so the curve goes Up-Down-Up. Thus, $x=a$ is the local Maximum ($p$). $x=2a$ is the local Minimum ($q$).

Apply condition $p^2=q$: $(a{)}^2=2a$ $a^2-2a=0⟹a(a-2)=0$. Since $a>0$, we must have $a=2$.