$a)q=4^{\sqrt{3}-1}:\frac{1}{4}=4^{\sqrt{3}-1}:4^{-1}=4^{\sqrt{3}-1-\left(-1\right)}=4^{\sqrt{3}}={\left(2^2\right)}^{\sqrt{3}}={\left(2^{\sqrt{3}}\right)}^2\approx {\left(3,32\right)}^2>3^2=9$  

$q>9\Rightarrow q\notin \left(3,6\right)$