Answer
$5$
Work Step by Step
Note that $\sqrt{6} = 6^{\frac{1}{2}}$.
Write $\sqrt{6}$ as $6^{\frac{1}{2}}$ to obtain:
$6^{\frac{x-3}{4}}=6^{\frac{1}{2}}$
Use the rule $a^m=a^n \longrightarrow m=n$ to obtain:
$\dfrac{x-3}{4} = \dfrac{1}{2}$
Cross-multiply to obtain:
$2(x-3) = 4(1)
\\2x-6=4$
Add 6 on both sides of the equation to obtain:
$2x=10$
Divide 2 on both sides of the equation to obtain:
$x = 5$
