The most basic compound among the following is

In aqueous medium the basic strength of an amine depends on the ease with which the nitrogen donates its lone pair to a proton, i.e. on the electron-density present on nitrogen.

Key ideas that govern electron-density on nitrogen:
1. +I (electron-releasing) groups increase basicity by pushing electrons toward N.
2. -I or -M (electron-withdrawing) groups decrease basicity.
3. If the lone pair participates in resonance (conjugation) with an aromatic ring or a carbonyl group, it becomes less available for protonation, lowering basicity.

Let us apply these ideas to the four given compounds:

Case 1: Benzylamine
Structure: $$C_6H_5CH_2NH_2$$.
The NH2 group is attached to the benzylic carbon, not directly to the aromatic ring. Hence its lone pair is not involved in resonance with the benzene ring. The neighbouring $$CH_2$$ exerts a weak +I effect, so nitrogen retains almost the same basicity as in a typical aliphatic amine. Therefore benzylamine is a comparatively strong base.

Case 2: Aniline
Structure: $$C_6H_5NH_2$$.
Here the lone pair on nitrogen is in conjugation with the π-system of the benzene ring, forming resonance structures such as $$C_6H_5{-}NH_2^{+}\!\!=\!\!C_6H_5^{-}$$. This delocalisation withdraws electron density from N, so aniline is much less basic than aliphatic amines like methyl- or benzylamine.

Case 3: Acetanilide
Structure: $$C_6H_5NHCOCH_3$$.
Because the nitrogen is part of an amide link (-NH-CO-), its lone pair is strongly delocalised toward the carbonyl group $$\left( O{=}\!C{-}N \right)$$. Resonance with a carbonyl is more powerful than with an aromatic ring, so the lone pair becomes even less available. Hence acetanilide is markedly less basic than aniline.

Case 4: p-Nitroaniline
Structure: $$p{-}O_2N{-}C_6H_4NH_2$$.
The -NO2 group at para position is a strong -M and -I substituent. It pulls electron density away from the ring and, through the ring, also from the nitrogen lone pair (which is already involved in resonance with the ring). This further decreases basicity relative to aniline.

Ordering the compounds from highest to lowest basicity:
$$\text{Benzylamine} \gt \text{Aniline} \gt p\text{-Nitroaniline} \gt \text{Acetanilide}$$

Therefore, the most basic compound is benzylamine.

Option B which is: Benzylamine