To solve the equation \( 3 | a - 4 | = 12 \), we first isolate the absolute value term:
\[ | a - 4 | = \frac{12}{3} = 4. \]
Now, we can set up the two cases for the equation inside the absolute value:
- \( a - 4 = 4 \)
- \( a - 4 = -4 \)
Now we solve each case:
Case 1: \[ a - 4 = 4 \ a = 4 + 4 = 8. \]
Case 2: \[ a - 4 = -4 \ a = -4 + 4 = 0. \]
Thus, the two solutions are \( a = 8 \) and \( a = 0 \). Therefore, the solutions can be represented as the pair \( (0, 8) \).