There are seven different dichlorides, including stereoisomers, that can give 1,4-dimethyl cyclohexane through the Wurtz coupling reaction with an ethereal solution of sodium. Let's break down the steps to understand why this is the correct answer.

1. Understanding the Wurtz coupling reaction:
The Wurtz coupling reaction is a method used to synthesize alkanes by reacting alkyl halides with sodium metal. In this reaction, the sodium metal abstracts a halogen atom from one alkyl halide and forms a radical, which then reacts with another alkyl halide to form a carbon-carbon bond. In the case of dichlorides, two molecules of alkyl halides react to give a longer alkane with two chlorine atoms replaced by carbon-carbon bonds.

2. Analyzing the given molecule:
The given molecule is 1,4-dimethyl cyclohexane. Let's break it down:
- The cyclohexane ring has six carbons, numbered from 1 to 6.
- There are two methyl groups attached to the carbons at positions 1 and 4.

3. Identifying the possible dichlorides:
To form 1,4-dimethyl cyclohexane, we need to replace two chlorine atoms with carbon-carbon bonds. Here are the possible dichlorides:

a) 1,4-dichlorocyclohexane:
- This is the simplest dichloride that can give 1,4-dimethyl cyclohexane.
- Both chlorine atoms are attached to carbons at positions 1 and 4.

b) 1-chloro-4-methylcyclohexane and 4-chloro-1-methylcyclohexane:
- In both of these dichlorides, one chlorine atom is attached to the carbon at position 1, and the other chlorine atom is attached to the carbon at position 4.
- The methyl group is attached to the carbon at the other position (either 4 or 1).

c) 1,2-dichlorocyclohexane and 1,6-dichlorocyclohexane:
- In these dichlorides, one chlorine atom is attached to the carbon at position 1, and the other chlorine atom is attached to either position 2 or 6.
- There are no methyl groups attached in these dichlorides.

d) 1,3-dichlorocyclohexane and 1,5-dichlorocyclohexane:
- In these dichlorides, one chlorine atom is attached to the carbon at position 1, and the other chlorine atom is attached to either position 3 or 5.
- There are no methyl groups attached in these dichlorides.

4. Counting the total number of dichlorides:
Adding up all the possibilities, we have a total of seven different dichlorides that can give 1,4-dimethyl cyclohexane through the Wurtz coupling reaction.

In summary, there are seven different dichlorides, including stereoisomers, that can give 1,4-dimethyl cyclohexane through the Wurtz coupling reaction with an ethereal solution of sodium. These dichlorides include 1,4-dichlorocyclohexane, 1-chloro-4