$a)\left|4\frac{1}{2}-\frac{11}{2}\right|=\left|4\frac{1}{2}-5\frac{1}{2}\right|=\left|-1\right|=1$

$b)\left|3-4\sqrt{3}\right|=-\left(3-4\sqrt{3}\right)=-3+4\sqrt{3}=4\sqrt{3}-3\left(bo3-4\sqrt{3}<0\right)$

$c)\left|6\frac{1}{3}-8\frac{3}{5}\right|-\left|8\frac{2}{5}-6\frac{1}{3}\right|=-\left(6\frac{1}{3}-8\frac{3}{5}\right)-\left(8\frac{2}{5}-6\frac{1}{3}\right)=-6\frac{1}{3}+8\frac{3}{5}-8\frac{2}{5}+6\frac{1}{3}=\frac{1}{5}$

$d)\left|\sqrt{7}-2\right|\cdot \left|-\sqrt{7}-2\right|=\left(\sqrt{7}-2\right)\cdot \left(-\left(-\sqrt{7}-2\right)\right)=\left(\sqrt{7}-2\right)\cdot \left(\sqrt{7}+2\right)={\sqrt{7}}^2-2^2=7-4=3$