The given problem requires finding the first number out of four, given that the average of the first three numbers is 19 and the average of the last three numbers is 20. It is also given that the last number is 2.

To solve this problem, we can use the concept of averages and the formula for calculating averages.

Understanding the Problem:
We are given 4 numbers, let's call them A, B, C, and D. We need to find the value of A.

Using the Average Formula:
The average of a set of numbers is calculated by summing all the numbers and dividing the sum by the count of numbers. We can use this concept to solve the problem.

Breaking Down the Averages:
1. The average of the first three numbers is 19.
- (A + B + C) / 3 = 19

2. The average of the last three numbers is 20.
- (B + C + D) / 3 = 20

Substituting the Known Values:
Since the last number is given as 2, we can substitute it into the second equation:
- (B + C + 2) / 3 = 20

Using the First Equation:
We can solve the first equation to find the value of (A + B + C):
- (A + B + C) = 19 * 3
- (A + B + C) = 57

Substituting in the Second Equation:
Now, we can substitute the value of (A + B + C) into the second equation:
- (57 + 2) / 3 = 20
- 59 / 3 = 20

Solving for B + C:
To solve for B + C, we can multiply both sides of the equation by 3:
- 59 = 20 * 3
- 59 = 60

Understanding the Contradiction:
We have reached a contradiction in the equation. Since 59 does not equal 60, it means that our initial assumption was incorrect.

Conclusion:
Therefore, there is no valid solution to the given problem. The question seems to have a mistake or an inconsistency in the given information.