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

1. N-Ethylethanamine (Diethylamine) is a secondary aliphatic amine. Due to the electron-donating inductive effect (+I effect) of two ethyl groups and favourable solvation, it is the strongest base among the given options and has the lowest $pK_b$ value of 3.0. [(d) $\rightarrow$ (iv)]
2. Methenamine (Methylamine) is a primary aliphatic amine. It has one methyl group (+I effect), making it a stronger base than ammonia but weaker than secondary amines. Its $pK_b$ value is 3.38. [(c) $\rightarrow$ (i)]
3. Phenylmethanamine (Benzylamine) has the amino group attached to an $sp^3$ hybridized benzylic carbon. The lone pair on nitrogen is not delocalized into the benzene ring. It is moderately basic but slightly less basic than simple aliphatic amines due to the mild electron-withdrawing (-I) effect of the phenyl group. Its $pK_b$ value is 4.70. [(b) $\rightarrow$ (iii)]
4. Benzenamine (Aniline) is an aromatic primary amine. The lone pair of electrons on the nitrogen atom is delocalized over the benzene ring via resonance, making it significantly less available for protonation. Thus, it is the weakest base and has the highest $pK_b$ value of 9.38. [(a) $\rightarrow$ (ii)]

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