Which two numbers should be interchanged to make the given equation correct?

120 ÷ 12 x 6 + 24 - 15 = 27

12 and 24

By interchanging 12 and 24 in the equation: 

120 ÷ 12 x 6 + 24 - 15 = 27, the equation becomes

   120 ÷ 24 x 6 + 12 - 15 = 27

Using BODMAS rule,

⇒  5 x 6 + 12 - 15 = 27

⇒  30 + 12 - 15 = 27

          LHS = RHS

The equation becomes correct.