1. The problem is to simplify the expression $2 | - 14 + 7 | - (-10)$. 2. Recall that the absolute value $|x|$ is the distance of $x$ from zero on the number line, so it is always non-negative. 3. First, simplify inside the absolute value: $-14 + 7 = -7$. 4. Then, find the absolute value: $|-7| = 7$. 5. Substitute back into the expression: $2 \times 7 - (-10)$. 6. Multiply: $2 \times 7 = 14$. 7. Subtracting a negative is the same as adding: $14 - (-10) = 14 + 10 = 24$. 8. Therefore, the simplified value of the expression is $24$.