The correct answer is (c) to teach.
"Governments are starting programmes to teach adults how to read and write." (Infinitive of purpose)
After nouns like programmes, plans, attempts, we use infinitive (to + verb) to express purpose or function. Options (a) and (b) use relative clauses incorrectly without proper antecedent agreement, and (d) is a past continuous form which doesn't fit here grammatically.