To compute $\det(A)$ for a $3 \times 3$ matrix, a student performs row operations:

• $R_2 \to R_2 - 3R_1$ (subtract 3 times row 1 from row 2) • $R_3 \to \frac{1}{2}R_3$ (divide row 3 by 2)

After these operations, the resulting upper triangular matrix has determinant $12$. What is $\det(A)$?