#### Answer

See below

#### Work Step by Step

Let us simplify both sides.
The left is already simplified.
The right simplifies as follows
$$(x-6)(x-4) = x^2 -(6+4)x + (-6)(-4)$$
$$ = x^2-10x+24$$
Thus the mathematician probably forgot to account for the fact that two negatives multiplied together make a positive.
Let's do it properly,
$$x^2-10x-24 = x^2-12x+2x-24 = x(x-12)+2(x-12) = (x+2)(x-12)$$