To solve for \( x \) in the equation
\[ 102.5 ( x - 11.92 ) = 71.6, \]
we first divide both sides of the equation by 102.5 to isolate the term containing \( x \):
\[ x - 11.92 = \frac{71.6}{102.5}. \]
Now we calculate the right side:
\[ \frac{71.6}{102.5} \approx 0.6975609757. \]
Now substituting this back into the equation gives:
\[ x - 11.92 \approx 0.6975609757. \]
Next, we add \( 11.92 \) to both sides:
\[ x \approx 11.92 + 0.6975609757 \approx 12.6175609757. \]
Rounding this to three decimal places results in:
\[ x \approx 12.618. \]
Therefore, the rounded answer is:
\[ \boxed{12.618}. \]