To solve the expression \( \frac{3}{8} \times \frac{4}{9} \), you multiply the numerators together and the denominators together:
\[ \frac{3 \times 4}{8 \times 9} = \frac{12}{72} \]
Now, simplify \( \frac{12}{72} \) by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 12:
\[ \frac{12 \div 12}{72 \div 12} = \frac{1}{6} \]
Now, let's look at the provided answers:
- \( \frac{7}{72} \)
- \( \frac{12}{72} \) (which we saw earlier)
- \( \frac{12}{81} \)
- \( \frac{7}{17} \)
From the answers given, \( \frac{12}{72} \) is indeed present as one of the choices. So the correct response from the options provided is:
\( 12 \over 72 \)