Final answer:
The three consecutive even integers that satisfy the given conditions are 20, 22, and 24.
Step-by-step explanation:
The subject of this question is Mathematics, which involves solving an algebraic problem based on consecutive even numbers.
Let's denote the smallest of the three numbers as x. Then, the other two numbers will be x + 2 and x + 4, since they are consecutive even numbers following x. The problem statement gives us the equation: 3*x = 2*(x + 4) + 12.
Solving this equation we will get: 3x - 2x = 8 + 12 which simplifies to x = 20. So, the three consecutive even integers are 20, 22, and 24.
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