Question

Fill in the blank with the most appropriate answer. No miento___años.

Answer 1

No miento desde hace anos.
This sentence means - I haven't lied in years.
A is incorrect because it is the wrong sequence of words - should be desde hace, and not hace desde. Que is also wrong in this context - it wouldn't mean anything in this sentence. Desde would be used with words such as ayer (=yesterday), and not with a certain period of time (like anos = years). 

Answer 2

desde hace is the phrase that fits.

There you go.