Identify the structure

The compound is a benzene ring having two substituents:

• one chloro group, $-Cl$
• one methyl group, $-CH_3$

These are placed at the para positions relative to each other, i.e. positions $1$ and $4$.

Apply IUPAC naming rules

For a disubstituted benzene:

• Number the ring to give the lowest set of locants.
• If there is a tie, assign locant $1$ to the substituent that comes first in alphabetical order.

Here, the substituents are:

• chloro
• methyl

Alphabetically, chloro comes before methyl. So the correct IUPAC name is: $1\text{-chloro-}4\text{-methylbenzene}$

Hence, Option A is correct.

Check retained/common IUPAC name

The compound can also be named as a derivative of toluene:

• toluene = methylbenzene
• chloro group is at the para position

So the name is: $4\text{-chlorotoluene}$

Hence, Option B is also correct.

Examine Option C: $4$-methylchlorobenzene

This is not the proper IUPAC form. In benzene derivatives with two substituents, both substituents should be cited separately with benzene as parent, giving: $1\text{-chloro-}4\text{-methylbenzene}$ not "$4$-methylchlorobenzene".

So Option C is incorrect.

Examine Option D: $1$-methyl-$4$-chlorobenzene

Though the locants are $1,4$, in a tie the substituent cited first alphabetically should get locant $1$. Since chloro comes before methyl, the correct numbering must be: $1\text{-chloro-}4\text{-methylbenzene}$ not $1\text{-methyl-}4\text{-chlorobenzene}$

So Option D is incorrect.

Final answer

The correct IUPAC/accepted names are:

• A. $1$-chloro-$4$-methylbenzene
• B. $4$-chlorotoluene