#### Answer

$x=\frac{1}{2}$

#### Work Step by Step

We rewrite the 8 on the right side, so that the base is $2$ on both sides.
$2^{6-3x}=8^{x+1}$
$2^{6-3x}=(2^3)^{x+1}$
By the law of exponents: $(a^x)^y=a^{xy}$
$(2^3)^{x+1}=2^{3x+3}$
Thus, the given equation is equivalent to:
$2^{6-3x} = 2^{3x+3}$
Then we set the exponents equal, because the two sides are equal only if the powers are equal too: if $b^m=b^n$ and $b \ne0$ , $b \ne1$ then $m=n$
$6-3x=3x+3
6-3=3x+x$
$3=6x$
$\frac{3}{6}=\frac{6x}{6}
\\\frac{1}{2}=x$