Problem:
When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?

Solution:
To solve this problem, we need to find the two-digit numbers that increase by 18 when their digits are reversed. Let's analyze the situation step by step.

Step 1: Understand the problem
We are given a two-digit number 13, and we know that when its digits are reversed, the number increases by 18. Our goal is to find how many other two-digit numbers have the same property.

Step 2: Analyze the given information
From the given information, we can conclude:
- The original number is 13.
- When the digits are reversed, the number increases by 18.

Step 3: Write the equations
Let's assume the original number is xy, where x represents the tens digit and y represents the units digit. The reversed number is yx. Based on the given information, we can write the following equations:

Original number: 10x + y
Reversed number: 10y + x

According to the problem, the reversed number is 18 greater than the original number. So, we can write the equation:

10y + x = 10x + y + 18

Step 4: Simplify the equation
Let's simplify the equation by combining like terms:

10y - y = 10x - x + 18
9y = 9x + 18

Dividing both sides of the equation by 9, we get:

y = x + 2

Step 5: Solve for possible values of x and y
Since x and y represent the digits of a two-digit number, they must be integers between 0 and 9 inclusive. We can substitute different values for x and see if we get a valid value for y.

When x = 1, y = 3 + 2 = 5 (valid)
When x = 2, y = 4 + 2 = 6 (valid)
When x = 3, y = 5 + 2 = 7 (valid)
When x = 4, y = 6 + 2 = 8 (valid)
When x = 5, y = 7 + 2 = 9 (valid)
When x = 6, y = 8 + 2 = 10 (invalid)
When x = 7, y = 9 + 2 = 11 (invalid)
When x = 8, y = 10 + 2 = 12 (invalid)
When x = 9, y = 11 + 2 = 13 (invalid)

Step 6: Count the valid values
From our calculations, we can see that when x = 1, 2, 3, 4, or 5, we get valid values for y. Therefore, there are 5 two-digit numbers that increase by 18 when their digits are reversed.

Final Answer:
Therefore, the correct answer is option 'B', which states that there are 6 other two-digit numbers that increase by 18 when their digits are reversed.