The least basic among the following nitrogen compounds is

Basicity electron $\mathrm{\alpha }$ density on nitrogen atom

$-{\mathrm{C}}_6{\mathrm{H}}_5$ group is an -I effect group. So, it decreases the electron density on nitrogen atom and as a result decreases its basicity.

Thus, more the number of phenyl groups, lesser is the basicity of that compound.

Therefore, the order of basicity for the given compounds are

${\mathrm{NH}}_3>{\mathrm{C}}_6{\mathrm{H}}_5{\mathrm{NH}}_2>{\left({\mathrm{C}}_6{\mathrm{H}}_5\right)}_2\mathrm{NH}>{\left({\mathrm{C}}_6{\mathrm{H}}_5\right)}_3\mathrm{N}$

Clearly, ${\left({\mathrm{C}}_6{\mathrm{H}}_5\right)}_3 \mathrm{N}$ is the least basic among them.