To solve for \( x \) in the equation
\[ 102.5(x - 11.92) = 71.6, \]
we first divide both sides by 102.5:
\[ x - 11.92 = \frac{71.6}{102.5}. \]
Calculating the right side:
\[ \frac{71.6}{102.5} \approx 0.6985. \]
Now, we can add \( 11.92 \) to both sides:
\[ x = 11.92 + 0.6985. \]
Calculating this gives:
\[ x \approx 12.6185. \]
Rounding to three decimal places:
\[ x \approx 12.619. \]
The correct answer is:
12.619