First find the volume of the cylinder:

$\displaystyle{V}=\pi{{r}}^{{2}}{h}=\pi{{\left({10}\right)}}^{{2}}\cdot{6}\approx{3.14}\cdot{600}={1},{884}\usepackage{cmbright}\Huge\$

Then find the volume of the hole shaped like a rectangular prism:

$\displaystyle{V}={l}\cdot{w}\cdot{h}={4}\cdot{4}\cdot{6}={96}\usepackage{cmbright}\Huge\$

Subtract the volume of the hole from the volume of the cylinder: $\displaystyle{1},{884}-{96}={1},{788}\usepackage{cmbright}\Huge\$

The volume of the solid is 1,788 cubic yards.