To solve the equation \( \frac{1}{4}(2x - 4) = 14 \), we first distribute \( \frac{1}{4} \) to the terms inside the parentheses:
\[ \frac{1}{4} \cdot 2x - \frac{1}{4} \cdot 4 \]
Calculating these gives:
\[ \frac{2x}{4} - \frac{4}{4} = \frac{x}{2} - 1 \]
So, we can rewrite the equation as:
\[ \frac{x}{2} - 1 = 14 \]
Next, we will isolate \( x \) by adding 1 to both sides:
\[ \frac{x}{2} = 14 + 1 \]
This simplifies to:
\[ \frac{x}{2} = 15 \]
Now, we multiply both sides by 2 to solve for \( x \):
\[ x = 15 \cdot 2 \]
So,
\[ x = 30 \]
Thus, the final result is:
\[ \boxed{30} \]