Remember that the subordination index (from Goldman-Eisler et al. 1965) is calculated by dividing the number of subordinate clauses by the number of total clauses. A subordinate clause is a clause (in simple terms, a string of words containing a verb) that modifies or tells us about something in the main clause. In the answers below, the subordinate clauses are given in red and followed by ]. The main clause is in blue. Add these together to get the total number of clauses.
1. Because he was convinced] she liked it], the man bought his wife a CD of a symphony they had heard on the radio].
Note that the second subordinate clause tells us what he was convinced about, i.e. tells us something about the first subordinate clause.
Number of subordinate clauses = 3; total clauses = 4; subordination index = 3/4, i.e. 0.75
2. They listened to it the next day.
No subordinate clauses! One clause in total. Subordination index = 0/1, i.e. 0.00
3. She took it back because it was not the symphony] they had heard].
Number of subordinate clauses = 2; total clauses =3; subordination index = 2/3 , i.e. 0.67
4. The shop replaced it with the one the man should have bought].
Number of subordinate clauses = 1; total clauses =2; subordination index = 1/2 , i.e. 0.50
Note also that subordinate clauses are often introduced by coordinating words such as because or which. However they sometimes are not, but when they are not you can often put in a coordinating word. So in 1 the second subordinate clause could be introduced by that and the third one by which, without affecting the meaning.