To determine which ordered pair is part of the solution set for the equation \( y = 4x + 2 \), we need to substitute \( x \) with 3 in the equation and calculate the corresponding \( y \) value.
Substituting \( x = 3 \):
\[ y = 4(3) + 2 \] \[ y = 12 + 2 \] \[ y = 14 \]
Now, we can check which of the given ordered pairs matches \( (3, 14) \):
- \( (3, 12) \) → \( y \) value is 12 (not a solution)
- \( (3, 7) \) → \( y \) value is 7 (not a solution)
- \( (3, 45) \) → \( y \) value is 45 (not a solution)
- \( (3, 14) \) → \( y \) value is 14 (this is the solution)
Therefore, the correct option is \( (3, 14) \).