To factorize 4a\(^2\) - 9b\(^2\), we can use the difference of squares formula, which states that a\(^2\) - b\(^2\) = (a+b) (a-b). We just need to recognize that 4a\(^2\) is a\(^2\) multiplied by 4, and 9b\(^2\) is b\(^2\) multiplied by 9. Then we have:
4a\(^2\) - 9b\(^2\) = (2a)\(^2\) - (3b)\(^2\) = (2a + 3b) (2a - 3b)
Therefore, the correct answer is (2a+3b) (2a-3b).