Afarmer here's a weather report saying that temperatures will be decreasing approximately 6∘ 6∘ every hour for the next 5 hours. what signed number represents the total change in temperature expected over the next 5 hours

Because temperature is decreasing we can say that after one hour new temperature is -6° from starting temperature.

After 5 hours temperature will drop:
5*(-6) = -30 because temperature decrease is constant on each hour.

The answer is -30°