To expand fractions for subtraction, it is essential to have a common denominator. The denominators of the fractions in question are 6 and 9, with the least common denominator being 18. The first fraction, $\frac{11}{6}$, is expanded by multiplying by 3 to become $\frac{33}{18}$, while the second fraction, $\frac{7}{9}$, is expanded by multiplying by 2 to become $\frac{14}{18}$. This allows for the subtraction of the numerators, resulting in $\frac{19}{18}$. Understanding this process is crucial for performing operations with fractions effectively.