The basic strength of an amine is inversely proportional to its $pK_b$ value. A lower $pK_b$ value indicates a stronger base.

1. N-Methylmethanamine (dimethylamine) is a secondary aliphatic amine. It is the strongest base among the given choices due to the electron-donating inductive effect (+I effect) of two methyl groups and favourable solvation effects. Therefore, it has the lowest $pK_b$ of 3.27. [(a) $\rightarrow$ (iv)]
2. Ammonia ($NH_3$) lacks alkyl groups but also lacks an electron-withdrawing aryl group. It is less basic than aliphatic amines but more basic than aromatic amines, having a $pK_b$ of 4.75. [(b) $\rightarrow$ (iii)]
3. Benzenamine (aniline) is a primary aromatic amine. The lone pair of electrons on the nitrogen is delocalised over the benzene ring, making it a much weaker base. Its $pK_b$ is 9.38. [(d) $\rightarrow$ (ii)]
4. N-Methylaniline is a secondary aromatic amine. The presence of one methyl group (+I effect) increases the electron density on nitrogen slightly compared to aniline, making it slightly more basic. Hence, its $pK_b$ is lower than aniline at 9.30. [(c) $\rightarrow$ (i)]

Therefore, the correct matching is (a)-(iv), (b)-(iii), (c)-(i), (d)-(ii).