|2(x+1)+6|=10

Te equation will be true if what is between the absolute
value bars equals to +10 or if it equals -10.

So to remove absolute value bars, write two equations
indicating both cases and solve them separately:

2(x+1)+6 = 10        2(x+1)+6 = -10
  2x+2+6 = 10          2x+2+6 = -10
    2x+8 = 10            2x+8 = -10
      2x = 2               2x = -18
       x = 1                x = -9

Solution: {-9,1}, not any you listed, maybe there is a typo in
either a. or d.

Edwin