How many two-digit counting numbers are less than 30 or a multiple of 20?

To find the two-digit counting numbers less than 30, we consider the numbers from 10 to 29, which gives us 20 two-digit numbers. The multiples of 20 that are two-digit numbers are 20. Since 20 is already included in the count of two-digit numbers less than 30, the total remains 20. Therefore, there are 20 two-digit counting numbers that are either less than 30 or a multiple of 20.