Solution:
Let's represent the three consecutive even numbers as x, x+2, and x+4.

According to the problem, the sum of these three numbers is 60:
x + (x+2) + (x+4) = 60.
Combining like terms, we can simplify the equation:
3x + 6 = 60.
Subtracting 6 from both sides:
3x = 54.
Dividing both sides by 3:
x = 18.

Therefore, the three consecutive even numbers are 18, 20, and 22.