Step 1: Recall factors affecting basicity of anilines.
Basicity depends on availability of lone pair on nitrogen.
Electron donating groups increase basicity, while electron withdrawing groups decrease it.
Step 2: Analyze substituents.
(A) and (B): Halogens show –I effect, reducing basicity.
(C): Nitro groups have strong –I and –R effects, greatly reducing basicity.
(D): Methyl groups show +I effect, increasing electron density on nitrogen.
Step 3: Conclusion.
2,4–Dimethylaniline is the most basic among the given options.