We are given the expression \( 6 - 2x |10 - x^4| \) and the value \( x = -4 \). Let's substitute \( x = -4 \) into the expression and simplify.

### Step 1: Substituting \( x = -4 \) into the expression
\[
6 - 2(-4) |10 - (-4)^4|
\]

### Step 2: Simplify \( (-4)^4 \)
\[
(-4)^4 = 256
\]

### Step 3: Substitute \( 256 \) into the expression
\[
6 - 2(-4) |10 - 256|
\]
\[
= 6 - 2(-4) |-246|
\]
Since the absolute value of \( -246 \) is \( 246 \), we now have:
\[
= 6 - 2(-4) \times 246
\]

### Step 4: Simplify the multiplication
\[
= 6 + 8 \times 246
\]
\[
= 6 + 1968
\]

### Step 5: Final result
\[
= 1974
\]

So, the value of the expression when \( x = -4 \) is **1974**.

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Simplify the expression \( 5 - 3x |2 - x^3| \) for \( x = -2 \).
2. What is the absolute value of \( |3x^2 - 8x + 4| \) when \( x = 5 \)?
3. Evaluate \( 7 - 2x |4 - x^2| \) for \( x = 3 \).
4. Simplify \( 2 + x |6x^2 - 12| \) for \( x = 1 \).
5. Solve \( 4x - |x^2 - 9| = 0 \) for \( x \).

**Tip:** When simplifying expressions with absolute values, always handle the absolute value carefully by considering the sign of the value inside it.

Learn how to evaluate the expression 6 - 2x |10 - x^4| when x = -4 with a detailed step-by-step solution. This problem involves algebraic concepts such as substitution and absolute value properties. Suitable for students in Grades 8-10.

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