Question

6cos x-6sin x=3.sqrt6

Answer 1

Divide by 6
$cos x - sin x = \frac{\sqrt{6}}{2}$

Square both sides
$cos^2 x -2 sin x cos x + sin^2 x = \frac{3}{2}$

Simplify Left side using Trig identities: (Pythagorean, Double Angle)
$1 - sin (2x) = \frac{3}{2}$

Solve for x:
$sin (2x) = -\frac{1}{2} \\ \\ 2x = \frac{7 \pi}{6}, \frac{11 \pi}{6} \\ \\ x = \frac{7 \pi}{12}, \frac{11 \pi}{12}$