Answer
$x=3$
Work Step by Step
Note that $64=4^3$. Thus, the given equation is equivalent to:
$\left(\dfrac{1}{4}\right)^x = \dfrac{1}{4^3}
\\\left(\dfrac{1}{4}\right)^x = \left(\dfrac{1}{4}\right)^3$
Use the rule $a^m=a^n \longrightarrow m = n$ to obtain:
$x = 3$