Answer
$(-\infty,2)$.
The number line is shown below.
Work Step by Step
The given expression is
$\Rightarrow 3(4x-6)<4-\{5x-[6x-(4x-(3x+2))]\}$
Apply distributive property and clear the inner parentheses.
$\Rightarrow 12x-18<4-\{5x-[6x-(4x-3x-2)]\}$
Apply distributive property and clear the parentheses.
$\Rightarrow 12x-18<4-\{5x-[6x-4x+3x+2]\}$
Add like terms.
$\Rightarrow 12x-18<4-\{5x-[5x+2]\}$
Apply distributive property and clear the square bracket.
$\Rightarrow 12x-18<4-\{5x-5x-2\}$
Add like terms.
$\Rightarrow 12x-18<4-\{-2\}$
Apply distributive property and clear the curly bracket.
$\Rightarrow 12x-18<4+2$
Add like terms.
$\Rightarrow 12x-18<6$
Add $18$ to both sides.
$\Rightarrow 12x-18+18<6+18$
Simplify.
$\Rightarrow 12x<24$
Divide both sides by $12$.
$x<2$
