Answer
$x=6$
Work Step by Step
For $x\gt 0$ and $a$ a positive constant other than 1,
$\log_{a}x$ is the exponent to which $a$ must be raised in order to get $x$.
Thus, $\log_{a}x=m$ means $a^{m}=x$
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By definition, $\log_{4}(3x-2)=2$ means
$4^{2}=3x-2$
$16=3x-2$
$18=3x$
$6=x$