1. The problem asks to find the value of $u$ in the equation $$9^{12} = 3^u.$$\n\n2. We start by expressing 9 as a power of 3 because both sides should have the same base to compare exponents easily. Since $$9 = 3^2,$$ we rewrite the left side as $$9^{12} = (3^2)^{12}.$$\n\n3. Using the power of a power rule, $$(a^m)^n = a^{m \times n},$$ we simplify the left side: $$(3^2)^{12} = 3^{2 \times 12} = 3^{24}.$$\n\n4. Now the equation is $$3^{24} = 3^u.$$\n\n5. Since the bases are the same and the expressions are equal, their exponents must be equal: $$24 = u.$$\n\n6. Therefore, the value of $u$ is $$\boxed{24}.$$