To find how many goals Tom needs to make in order to have an equivalent fraction of goals to Andre’s \( \frac{4}{6} \), we first simplify Andre’s fraction.
The fraction \( \frac{4}{6} \) can be simplified by dividing both the numerator and the denominator by 2:
\[ \frac{4 \div 2}{6 \div 2} = \frac{2}{3} \]
Now, we want Tom to have the same ratio of goals made to kicks taken, which is \( \frac{2}{3} \). Tom takes 12 kicks, so we can set up the equation:
\[ \frac{g}{12} = \frac{2}{3} \]
where \( g \) is the number of goals Tom needs to make. To solve for \( g \), we can cross-multiply:
\[ 3g = 2 \times 12 \]
Calculating the right side:
\[ 3g = 24 \]
Now, divide both sides by 3:
\[ g = \frac{24}{3} = 8 \]
Therefore, Tom needs to make 8 goals to have an equivalent fraction of goals as Andre.