There is no component make to in this sentence.
Turning the relevant phrase into its own sentence, we get
The private sector can make a contribution to enhancing cultural diversity.
Here, contribution is a direct object of make, and to enhancing cultural diversity is a prepositional phrase that modifies contribution.
So in the original sentence, "that the private sector can make ..." is a relative clause that modifies contribution; "contribution" is the object of the relative clause; and "to enhancing cultural diversity" is a prepositional phrase modifying contribution.