The range of a set of numbers is the difference between the largest and smallest numbers in the set.

The mode of a set of numbers is the number that appears most frequently.

Let's first find the range:

Arrange the numbers in ascending order: 4, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10

The smallest number is 4, and the largest number is 10.

Range = Largest number - Smallest number = 10 - 4 = 6

Now, let's find the mode (the number that appears most frequently):

Count the frequency of each number:

- 4 appears 1 time

- 5 appears 1 time

- 6 appears 2 times

- 7 appears 3 times

- 8 appears 3 times

- 9 appears 5 times

- 10 appears 7 times

The mode is the number 10 since it appears the most times (7 times).

Now, calculate the sum of the range and the mode:

Sum = Range + Mode = 6 + 10 = 16

Therefore, the sum of the range and the mode of the given set of numbers is 16.