Step 1: Recall effect of alkyl groups.
Alkyl groups release electrons by +I effect, increasing electron density on N and hence its basicity.
Step 2: Compare.
- (A) Aniline (C$_6$H$_5$NH$_2$): Lone pair delocalized into ring, basicity decreases.
- (B) Dimethylamine: Strong +I effect, lone pair available, very basic.
- (C) Trimethylamine: Steric hindrance reduces basicity in aqueous solution.
- (D) Ammonia: Less basic than substituted alkyl amines.
Step 3: Conclusion.
Most basic among them is (CH$_3$)$_2$NH.