To answer this question, we need to know what like terms are. Like terms are terms whose variables and exponents are the same. The coefficients can be different, though. In this case, the like terms are -a²b and 5a²b (because of the definition above.
You haven't shared "the given value of x," or, if you have, you haven't drawn attention to it.
Just suppose we were to choose x = 4 as a possible solution and then try to find a value of the parameter k that would make x = 4 an actual solution.
2(4) + 4k - 9 = (4)(4) - (4) + 1
Then 8 + 4k - 9 = 16 - 4 + 1, or 4k - 1 = 13. Then 4k = 14, and k = 14/4, or (after reduction) k = 7/2
If the parameter k equals 7/2, then x = 4 is a solution to the given equation.
To check this out further, start with the proposed solution x = 5 and find k.