You can first use the fundamental trigonometric identity:
sin(x) ^2 + cos(x) ^2 = 1
=> cos(x) ^2 = 1 - sin(x) ^2
=> cos(x) ^2 = 1 - (-4/5)^2 = 1 - 16/25 = (25 - 16) / 25 = 9 /25
=> cos (x) = +/ - √ (9/25) = +/- 3/5
Now, analyze the sign.
In the fhird quadrant the cosine is negative, so the answer is cos(x) = - 3/5.
Answer: option C. - 3/5