I am going to assume the question says cos(x) = -4/5, but correct me if I am wrong.
If cos(x) = -4/5 it means there is a right triangle with adjacent side of 4, and hypotenuse of 5. The negative is because this triangle is located in the third quadrant (180o < x < 270o), in which cos is negative. The remaining leg of the triangle (the opposite side) has to be 3 (from the Pythagorean theorem). So we have a 3, 4, 5 right triangle. Tangent is opposite/adjacent, which in this case is 3/4. We also know that this number should be positive because tangent is positive in the third quadrant.
To find tan(2x) we need to use the trig identity:
tan(2x) = 2tan(x) / (1-tan2(x))
Substituting our value of tan(x) = 3/4 into this identity, we get:
tan(2x) = 2(3/4) / (1 - (3/4)2)
tan(2x) = (3/2) / (1 - 9/16)
tan(2x) = (3/2) / (7/16)
tan(2x) = (3/2) * (16/7)
tan(2x) = 48/14 = 24/7