#### Answer

$x=-2$

#### Work Step by Step

$4x+13-\{2x-[4(x-3)-5]\}=2(x-6)$
Simplify the expression inside brackets on the left side and the product on the right side:
$4x+13-\{2x-[4x-12-5]\}=2x-12$
$4x+13-\{2x-[4x-17]\}=2x-12$
Simplify the expression inside braces on the left side:
$4x+13-\{2x-4x+17\}=2x-12$
$4x+13-\{-2x+17\}=2x-12$
Simplify the left side:
$4x+13+2x-17=2x-12$
$6x-4=2x-12$
Take $2x$ to the left side and $4$ to the right side. Then, simplify:
$6x-2x=-12+4$
$4x=-8$
Take $4$ to divide the right side:
$x=-\dfrac{8}{4}$
$x=-2$