Answer
$$D = \left\{ {\left( {x,y} \right):x - 2y + 4 \geqslant 0} \right\}$$
Work Step by Step
$$\eqalign{
& h\left( {x,y} \right) = \sqrt {x - 2y + 4} \cr
& {\text{Because }}h{\text{ involves a square root}},{\text{ its domain consists of }} \cr
& {\text{ordered pairs }}\left( {x,y} \right){\text{ for which }}x - 2y + 4 \geqslant 0. \cr
& {\text{Therefore, the domain of }}h{\text{ is }}D = \left\{ {\left( {x,y} \right):x - 2y + 4 \geqslant 0} \right\} \cr} $$
