6ab(4b^2c + 3a^2).

To simplify the given expression, we can distribute the 6ab term to both terms inside the parentheses:

6ab(4b^2c + 3a^2) = (6ab)(4b^2c) + (6ab)(3a^2)

Simplifying further, we can multiply the coefficients and add the exponents with like bases:

(6ab)(4b^2c) = (6 * 4)(a * b)(b^2 * c) = 24ab^3c

Similarly,

(6ab)(3a^2) = (6 * 3)(a * a)(b * b) = 18a^2b^2

Therefore, the simplified expression is:

24ab^3c + 18a^2b^2