Let the numbers be (a - d), a, (a + d).

Now, sum of the numbers = 48

∴ (a - d) + a + (a + d) = 48

⇒ 3a = 48

⇒ a = 16

Now, we are given that,

Product of first and second terms exceeds 4 times the third term by 12.

⇒ (a - d) × a = 4(a + d) + 12

⇒ a² - ad = 4a + 4d + 12

On putting the value of a in the above equation, we get,

256 - 16d = 64 + 4d + 12

⇒ 20 d = 180

⇒ d = 9

∴ The numbers are a - d, a, a + d

i.e. the numbers are 7, 16, 25.