$$\frac{\frac{4\times 3}{11}}{\frac{2}{3}}+\frac{1}{2}$$
Multiply $4$ and $3$ to get $12$.$$\frac{\frac{12}{11}}{\frac{2}{3}}+\frac{1}{2}$$
Divide $\frac{12}{11}$ by $\frac{2}{3}$ by multiplying $\frac{12}{11}$ by the reciprocal of $\frac{2}{3}$.$$\frac{12}{11}\times \left(\frac{3}{2}\right)+\frac{1}{2}$$
Multiply $\frac{12}{11}$ times $\frac{3}{2}$ by multiplying numerator times numerator and denominator times denominator.$$\frac{12\times 3}{11\times 2}+\frac{1}{2}$$
Do the multiplications in the fraction $\frac{12\times 3}{11\times 2}$.$$\frac{36}{22}+\frac{1}{2}$$
Reduce the fraction $\frac{36}{22}$ to lowest terms by extracting and canceling out $2$.$$\frac{18}{11}+\frac{1}{2}$$
Least common multiple of $11$ and $2$ is $22$. Convert $\frac{18}{11}$ and $\frac{1}{2}$ to fractions with denominator $22$.$$\frac{36}{22}+\frac{11}{22}$$
Since $\frac{36}{22}$ and $\frac{11}{22}$ have the same denominator, add them by adding their numerators.$$\frac{36+11}{22}$$
Add $36$ and $11$ to get $47$.$$\frac{47}{22}$$