$$\frac{x-12}{5}+\frac{3x}{4}=\frac{x+6}{2}$$
$x=12$
$$4\left(x-12\right)+5\times 3x=10\left(x+6\right)$$
$$4x-48+5\times 3x=10\left(x+6\right)$$
$$4x-48+15x=10\left(x+6\right)$$
$$19x-48=10\left(x+6\right)$$
$$19x-48=10x+60$$
$$19x-48-10x=60$$
$$9x-48=60$$
$$9x=60+48$$
$$9x=108$$
$$x=\frac{108}{9}$$
$$x=12$$
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