Evaluate |6(-7)-4|-|-4|*|7|+8(3)

$| 6 (- 7) - 4 | - | - 4 | \cdot | 7 | + 8 (3)$

Simplify each term.

Multiply $6$ by $- 7$ .

$| - 42 - 4 | - | - 4 | \cdot | 7 | + 8 (3)$

Subtract $4$ from $- 42$ .

$| - 46 | - | - 4 | \cdot | 7 | + 8 (3)$

The absolute value is the distance between a number and zero. The distance between $- 46$ and $0$ is $46$ .

$46 - | - 4 | \cdot | 7 | + 8 (3)$

The absolute value is the distance between a number and zero. The distance between $- 4$ and $0$ is $4$ .

$46 - 1 \cdot 4 \cdot | 7 | + 8 (3)$

Multiply $- 1$ by $4$ .

$46 - 4 \cdot | 7 | + 8 (3)$

The absolute value is the distance between a number and zero. The distance between $0$ and $7$ is $7$ .

$46 - 4 \cdot 7 + 8 (3)$

Multiply $- 4$ by $7$ .

$46 - 28 + 8 (3)$

Multiply $8$ by $3$ .

$46 - 28 + 24$

Simplify by adding and subtracting.

Subtract $28$ from $46$ .

$18 + 24$

Add $18$ and $24$ .

$42$