Solution

There are $4$ married couples, so total persons are $8$.

You asked $7$ persons, and all gave different answers.

Maximum possible handshakes by one person are $6$ because a person cannot shake hands with himself or herself and cannot shake hands with spouse.

So the $7$ different answers must be:

$0,1,2,3,4,5,6$

Now, the person who shook $6$ hands must be paired with the person who shook $0$ hands.

Similarly,

$5$ is paired with $1$

$4$ is paired with $2$

The only remaining number is $3$.

So your spouse shook $3$ hands.

Final Answer: $ \boxed{(c)} $