$$\frac{ 6(x-2) }{ 5 } > \frac{ 10(2-x) }{ 3 }$$
$x>2$
$$3\times 6\left(x-2\right)>5\times 10\left(2-x\right)$$
$$18\left(x-2\right)>5\times 10\left(2-x\right)$$
$$18x-36>5\times 10\left(2-x\right)$$
$$18x-36>50\left(2-x\right)$$
$$18x-36>100-50x$$
$$18x-36+50x>100$$
$$68x-36>100$$
$$68x>100+36$$
$$68x>136$$
$$x>\frac{136}{68}$$
$$x>2$$
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