Correct Answer: Film : Producer

Solution : Given:
Food : Chef (The words are related to each other as the first word is a term that is formed or produced and the second word is a profession related to the first term.)

Let's check each option –
First option: Painter : Painting; Painting is painted by the painter. But the order of the terms is not correct.
Second option: Hospital : Doctor; Doctors work in the hospital. The hospital is not built by the doctor.
Third option: Farmer : Field; Farmers work in the field.
Fourth option: Film : Producer; The film is produced by the producer.

So, only the fourth option follows the same pattern as followed by the given pair. Hence, the fourth option is correct.