When I had to leave town due to office work, I had my brother to give food to my dog twice a day.

The proper grammar structure is "have someone do something". The causative "have + person + base verb" is the standard way to indicate that someone was asked or instructed to perform a task on another's behalf. The correct answer is therefore option A:" had my brother feed my dog"

The other options contain grammatical errors that make them incorrect. Option A: "had my brother to give food" incorrectly inserts "to," which disrupts the standard causative form. Option B: "had my brother giving" uses the -ing form, which suggests an ongoing action rather than the intended meaning of arranged responsibility. Option C: "had my brother who fed" incorrectly turns the phrase into a description rather than an instruction, changing the meaning entirely.