The sum of the digits of a two-digit number is 14, and the difference between the digits is 2. Which of the following can be that number?

68 or 86

Let x and y be the two digits. Then as per the question:
x + y = 14 ...... (i)
And, x - y = 2 .... (ii)
On, adding both the equations:

2x = 16, x = 8

On, subtracting both the equations:

2y = 12, y = 6

Thus, x = 8, y = 6

Hence, 68 or 86 can be the required number.

Or, We can check the answer option directly and find the answer as per given condition.