The reaction of chlorine (Cl2) with 1,4-dimethylcyclohexane (show three possible monochlorination products) *what?!*

I think the tertiary carbons are most reactive followed by secondary then primary.

I would start be defining which which 1,4-dimethylcyclohexane I was starting with, or considering a mixture of cis and trans?

The tertiary carbons are most reactive as DrBob says, so there are two possible products from attack at the tertiary carbon:
cis and trans 1-chloro-1,4-dimethyl cyclohexane.

Attack at the secondary carbon adjacent to one of the methyl groups will result in 2-chloro-1,4-dimethylcyclohexane. If you start with a mixture of the cis and trans there are eight possible products which are:

1R,2R,4R, 1-chloro-1,4-dimethyl cyclohexane.
1S,2R,4R, 1-chloro-1,4-dimethyl cyclohexane.
1R,2S,4R, 1-chloro-1,4-dimethyl cyclohexane.
1R,2R,4S, 1-chloro-1,4-dimethyl cyclohexane.
1R,2S,4S, 1-chloro-1,4-dimethyl cyclohexane.
1S,2R,4S, 1-chloro-1,4-dimethyl cyclohexane.
1S,2S,4R, 1-chloro-1,4-dimethyl cyclohexane.
1S,2S,4S, 1-chloro-1,4-dimethyl cyclohexane.

Attack at the primary carbon in one of the methyl groups will give
1-chloromethyl-4-methylcyclohexane. Again you have the possibility of cis and trans depending on the starting material.

There is of course a deliberate mistake. I meant to list the eight as

1R,2R,4R, 2-chloro-1,4-dimethyl cyclohexane

etc.

To determine three possible monochlorination products when chlorine (Cl2) reacts with 1,4-dimethylcyclohexane, we need to consider the possible substitution sites on the cyclohexane ring.

The reaction of chlorine with hydrocarbons like 1,4-dimethylcyclohexane is known as free radical chlorination, which occurs via a radical substitution mechanism. In this mechanism, chlorine radicals are formed by the homolytic cleavage of the chlorine molecule. These radicals then react with the hydrocarbon, substituting a hydrogen atom with a chlorine atom.

To identify the possible monochlorination products, we need to have an understanding of the cyclohexane structure.

A cyclohexane ring has a total of six carbon atoms, labeled C1 to C6. Additionally, in 1,4-dimethylcyclohexane, there are two methyl groups attached to the ring, specifically on carbon atoms C1 and C4.

Now, we can consider the three possible monochlorination products:

1. C1 is chlorinated: In this case, one of the hydrogen atoms on carbon atom C1 is substituted with a chlorine atom. The resulting compound would be 1-chloro-4-dimethylcyclohexane.

2. C4 is chlorinated: In this case, one of the hydrogen atoms on carbon atom C4 is substituted with a chlorine atom. The resulting compound would be 4-chloro-1-dimethylcyclohexane.

3. The methyl group on C1 is chlorinated: In this case, one of the methyl groups attached to carbon atom C1 is substituted with a chlorine atom. The resulting compound would be 1-chloro-4-(chloromethyl) cyclohexane.

These are the three possible monochlorination products that can be formed when chlorine reacts with 1,4-dimethylcyclohexane.