Given that cos(x) = -√6/4, we can find the value of cos(2x) using the double angle formula:

cos(2x) = 2cos^2(x) - 1

First, we need to find cos^2(x):
cos^2(x) = (-√6/4)^2
cos^2(x) = 6/16
cos^2(x) = 3/8

Now, we substitute this value back into the formula for cos(2x):

cos(2x) = 2(3/8) - 1
cos(2x) = 6/8 - 1
cos(2x) = 3/4 - 1
cos(2x) = -1/4

Therefore, cos(2x) = -1/4.