The correct answer is (6x+8)^2.
To factor the expression, we can use the perfect square pattern. The perfect square pattern states that a binomial of the form a^2 + 2ab + b^2 can be factored as (a+b)^2.
In this case, we have a=6x and b=8. So, we can factor the expression as follows:
```
36x^2 + 96x + 64 = (6x)^2 + 2(6x)(8) + (8)^2
= (6x + 8)^2
```