To find out how much of the cake was left after Aliyah's siblings and friends ate their portions, we can start by combining the fractions of the cake that were eaten.
Her siblings ate \( \frac{1}{4} \) of the cake, and her friends ate \( \frac{2}{3} \) of the cake.
First, we need to add these two fractions together. To do that, we need a common denominator. The least common multiple of 4 and 3 is 12.
Now we convert both fractions to have a denominator of 12:
\( \frac{1}{4} = \frac{3}{12} \)
\( \frac{2}{3} = \frac{8}{12} \)
Now we can add them:
\[ \frac{3}{12} + \frac{8}{12} = \frac{11}{12} \]
This means that \( \frac{11}{12} \) of the cake was eaten by her siblings and friends.
To find out how much of the cake is left, we subtract the amount eaten from the whole cake:
\[ 1 - \frac{11}{12} = \frac{1}{12} \]
So, the amount of cake left after the party is \( \frac{1}{12} \).
The answer is A. \( \frac{1}{12} \).