sqrt6+2sqrt6√6+2√6 can be simplified by multiplying the expression by its conjugate term which is =color(blue)(sqrt6-2sqrt6=√6−2√6
=(sqrt6+2sqrt6) * (color(blue)(sqrt6-2sqrt6))=(√6+2√6)⋅(√6−2√6) , here we can apply the below property:
(a+b)(a-b) = color(blue)((a^2-b^2)(a+b)(a−b)=(a2−b2)
=(sqrt6+2sqrt6) * (color(blue)(sqrt6-2sqrt6)) = (sqrt6)^2-(2sqrt6)^2=(√6+2√6)⋅(√6−2√6)=(√6)2−(2√6)2
=6 -24=6−24
=color(blue)(-18=−18