if a is real and the product of (a+6i)(5-31) is a real number, then find a

I think you might mean  this  ???

(a + 6i) ( 5 - 3i)

5a + 30i - 3ai  - 18i^2

5a + 30i - 3ai + 18

a =  10

Because

5 (10)  + 30i  -3(10)i + 18  =

50 + 30i - 30i + 18  =

68