1. **State the problem:** We are given values from Pascal's triangle and variables $a$ and $b$ located at specific positions. We need to find the value of the expression $4b - 3a + 12$. 2. **Recall Pascal's triangle properties:** Each number inside Pascal's triangle is the sum of the two numbers directly above it. 3. **Identify $a$ and $b$ in the triangle:** - The row with $a$ is the 2nd row (starting from 0): 1, 6, 15, $a$, 15, 6, 1. - The row with $b$ is the 3rd row: 8, $b$, 56, 70, 56, 28, 8. 4. **Find $a$:** Since $a$ is between 15 and 15 in the 2nd row, and each element is the sum of the two above it, $a$ corresponds to the 4th element in the 2nd row. The 1st row is: 1, 5, 10, 10, 5, 1 The 2nd row is: 1, 6, 15, $a$, 15, 6, 1 Using Pascal's rule: $$a = 10 + 15 = 25$$ 5. **Find $b$:** $b$ is the 2nd element in the 3rd row: 8, $b$, 56, 70, 56, 28, 8 Using Pascal's rule: $$b = 6 + 15 = 21$$ 6. **Calculate the expression:** $$4b - 3a + 12 = 4 \times 21 - 3 \times 25 + 12$$ $$= 84 - 75 + 12$$ $$= 21$$ **Final answer:** $21$