Let the ones digit be ‘a’ and tens digit be ‘b’.

Given, two-digit number is such that the product of its digits is 16.

⇒ ab = 16 --- (1)

Also, when 54 is subtracted from the number, the digits interchange their places

⇒ 10b + a – 54 = 10a + b

⇒ 9b – 9a = 54

⇒ b – a = 6

⇒ b = 6 + a

Substituting in 1

⇒ a × (6 + a) = 16

⇒ a² + 6a – 16 = 0

⇒ a² + 8a – 2a – 16 = 0

⇒ a(a + 8) – 2(a + 8) = 0

⇒ (a – 2)(a + 8) = 0

⇒ a = 2

Thus, b = 8

Number is 82