In[36]:= Reduce[2 Abs[2 x - 7] + 6 > 16, x, Reals]
Out[36]= x < 1 || x > 6
Please learn the syntax - it's worth it. You get an answer here because you used English syntax. You get (mostly) an answer from Mathematica if you use it's syntax correctly. Trust yourself, do it by hand first, than check the result with Mathematica.