sat-dog

Choice C is correct. Since each term of the given expression has a common factor of $6x^2{y}^2$, it may be rewritten as $6x^2{y}^2\left(x^6\right)+6x^2{y}^2\left(2\right)$, or $6x^2{y}^2(x^6+2)$.

Choice A is incorrect. This expression is equivalent to $12x^8{y}^2$, not $6x^8{y}^2+12x^2{y}^2$.

Choice B is incorrect. This expression is equivalent to $6x^6{y}^2$, not $6x^8{y}^2+12x^2{y}^2$.

Choice D is incorrect. This expression is equivalent to $6x^6{y}^2+12x^2{y}^2$, not $6x^8{y}^2+12x^2{y}^2$.