Let's solve the given algebraic expressions step-by-step by substituting the values:

Part (a)

Expression: $6 + 4(x - 4)^3$, for $x = 6$

1. Substitute $x = 6$: $6 + 4(6 - 4)^3$

2. Simplify inside the parentheses: $6 - 4 = 2$

3. Raise to the power of 3: $2^3 = 8$

4. Multiply by 4: $4 \times 8 = 32$

5. Add 6: $6 + 32 = 38$

Answer for (a): 38

Part (b)

Expression: $x^2 - 2(x - y)$, for $x = 9$ and $y = 3$

1. Substitute $x = 9$ and $y = 3$: $9^2 - 2(9 - 3)$

2. Calculate $9^2$: $9^2 = 81$

3. Simplify inside the parentheses: $9 - 3 = 6$

4. Multiply by 2: $2 \times 6 = 12$

5. Subtract from 81: $81 - 12 = 69$

Answer for (b): 69

Would you like any further details or have any questions?

Here are some related questions that might help you practice similar problems:

1. Evaluate $5 + 3(x + 1)^2$ for $x = 2$.
2. Find the value of $2x^3 - y^2$ for $x = 4$ and $y = 5$.
3. Simplify the expression $7 - 2(x - 3)^2$ when $x = 1$.
4. Evaluate $x^2 + y - z$ for $x = 7$, $y = 5$, and $z = 3$.
5. Calculate $3(x - 2)^3 + 4y$ for $x = 3$ and $y = 2$.

Tip: Always simplify the expression inside the parentheses before proceeding with powers or multiplication to reduce mistakes.