To multiply a fraction by a whole number, you multiply only the numerator (top number) of the fraction by the whole number and keep the denominator (bottom number) the same.
In this case, Lara multiplied \( \frac{4}{13} \) by 3:
\[ \frac{4 \times 3}{13} = \frac{12}{13} \]
However, she wrote \( \frac{12}{39} \), which is incorrect.
Now, let's simplify \( \frac{12}{39} \):
The greatest common divisor of 12 and 39 is 3, so:
\[ \frac{12 \div 3}{39 \div 3} = \frac{4}{13} \]
Thus, \( \frac{12}{39} \) simplifies back to \( \frac{4}{13} \), which means her answer is not correct as per the original multiplication.
Therefore, the response is:
No, she should have multiplied only the numerator by the whole number.