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

The electron density on the nitrogen atom increases with the presence of the electron-donating group and decreases with the presence of the electron-withdrawing group.

In acetanilide,

The Acetyl group is electron withdrawing in nature and as a result, it decreases the electron density on the nitrogen atom and therefore decreases its basicity.

In aniline,

There is no electron withdrawing or electron donating group in it. so, relative to the lone pair of the nitrogen atom of acetanilide it has more freedom to donate it.

Thus, acetanilide is less basic than aniline.

Hence, option (A) is correct.