To solve this problem, you just need to add the two functions together, making sure that you watch your signs.
f(x) + g(x) = (2x - 7) + (-6x -3)
After we simplify and combine like terms, we get:
f(x) + g(x) = 2x - 7 - 6x - 3
= -4x - 10
The domain is all real numbers because both of the functions being added together also have a domain of all real numbers.
Therefore, the answer you have selected (the last option) is correct.
Hope this helps!