Let the two-digit number be 10x + y, where x = tens digit, y = units digit.

Step 1: Product condition

x × y = 12 … (1)

Step 2: Interchange condition

If digits interchange, new number = 10y + x

Given: (10x + y) + 36 = (10y + x)

⇒ 9x – 9y = –36

⇒ x – y = –4 … (2)

Step 3: Solve equations

From (2): x = y – 4

Put in (1): (y – 4) × y = 12

⇒ y² – 4y – 12 = 0

⇒ (y – 6)(y + 2) = 0

⇒ y = 6 (since digit can’t be –2)

Then x = y – 4 = 2

Number = 10x + y = 10×2 + 6 = 26

✅ Final Answer: The number is 26.