Step 1: Basic strength of amines is determined by the electron-donating ability of the substituents attached to the nitrogen atom.
Step 2: As the number of methyl groups increases, the electron-donating ability increases, making the amine more basic.
Thus, \( {(CH}_3{)}_2{NH} \) is the most basic.
Step 3: The order of basic strength is \( {(CH}_3{)}_2{NH}>{CH}_3{NH}_2>{(CH}_3{)}_3{N}>{NH}_3 \).