If $4x^2 - 12x + a$ is the square of a binomial, then it must be of the form $(2x + b)^2$ for some constant $b$.
Expanding $(2x + b)^2$ gives $4x^2 + 4bx + b^2$.
Comparing this with $4x^2 - 12x + a$, we see that $4bx = -12x$, so $b = -3$.
Therefore, $(2x + b)^2 = (2x - 3)^2 = 4x^2 - 12x + 9$.
Thus, $a = \boxed{9}$.
The answer is: 9
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
If $a$ is a constant such that $4x^2 - 12x + a$ is the square of a binomial, then what is $a$?

### Answer:
