Thanks for showing your work above. The mistake that you make is that you included an x on the 15.
The problem starts: 15-10(x-4)-(3x+3)
You do a great job distributing the -10 and negative. The 15 just doesn't get an x.
15 - 10x + 40 - 3x - 3
(-10x - 3x) + (15 + 40 - 3)
Combing like terms: -13x + 52
It looks like you understand the concept of distributing and combining like terms very well. I know when answers don't match the back of the book, it can be very frustrating. Keep up the hard work/effort and I think you'll notice these types of mistakes diminishing.