$$\left(2-\frac{3}{2}\right)^{2}+\left(4+\frac{1}{2}-\frac{2}{3}\right)\times \left(\frac{12}{23}\right)-\left(1-\frac{1}{2}\right)^{2}$$
Subtract $\frac{3}{2}$ from $2$ to get $\frac{1}{2}$.$$\left(\frac{1}{2}\right)^{2}+\left(4+\frac{1}{2}-\frac{2}{3}\right)\times \left(\frac{12}{23}\right)-\left(1-\frac{1}{2}\right)^{2}$$
Calculate $\frac{1}{2}$ to the power of $2$ and get $\frac{1}{4}$.$$\frac{1}{4}+\left(4+\frac{1}{2}-\frac{2}{3}\right)\times \left(\frac{12}{23}\right)-\left(1-\frac{1}{2}\right)^{2}$$
Add $4$ and $\frac{1}{2}$ to get $\frac{9}{2}$.$$\frac{1}{4}+\left(\frac{9}{2}-\frac{2}{3}\right)\times \left(\frac{12}{23}\right)-\left(1-\frac{1}{2}\right)^{2}$$
Subtract $\frac{2}{3}$ from $\frac{9}{2}$ to get $\frac{23}{6}$.$$\frac{1}{4}+\frac{23}{6}\times \left(\frac{12}{23}\right)-\left(1-\frac{1}{2}\right)^{2}$$
Multiply $\frac{23}{6}$ and $\frac{12}{23}$ to get $2$.$$\frac{1}{4}+2-\left(1-\frac{1}{2}\right)^{2}$$
Add $\frac{1}{4}$ and $2$ to get $\frac{9}{4}$.$$\frac{9}{4}-\left(1-\frac{1}{2}\right)^{2}$$
Subtract $\frac{1}{2}$ from $1$ to get $\frac{1}{2}$.$$\frac{9}{4}-\left(\frac{1}{2}\right)^{2}$$
Calculate $\frac{1}{2}$ to the power of $2$ and get $\frac{1}{4}$.$$\frac{9}{4}-\frac{1}{4}$$
Subtract $\frac{1}{4}$ from $\frac{9}{4}$ to get $2$.$$2$$