## Answer :

1.

**Substitute the values into the expression:**

[tex]\[ 6 \cdot \left(\frac{1}{2}\right) \left((-1)^2 \cdot 2\right) \][/tex]

2.

**Calculate [tex]\( (-1)^2 \)[/tex]:**

[tex]\[ (-1)^2 = 1 \][/tex]

3.

**Substitute [tex]\( (-1)^2 = 1 \)[/tex] into the expression:**

[tex]\[ 6 \cdot \left(\frac{1}{2}\right) \left(1 \cdot 2\right) \][/tex]

4.

**Calculate [tex]\( 1 \cdot 2 \)[/tex]:**

[tex]\[ 1 \cdot 2 = 2 \][/tex]

5.

**Substitute [tex]\( 2 \)[/tex] into the expression:**

[tex]\[ 6 \cdot \left(\frac{1}{2}\right) \cdot 2 \][/tex]

6.

**Calculate [tex]\( \left(\frac{1}{2}\right) \cdot 2 \)[/tex]:**

[tex]\[ \left(\frac{1}{2}\right) \cdot 2 = 1 \][/tex]

7.

**Substitute [tex]\( 1 \)[/tex] into the expression:**

[tex]\[ 6 \cdot 1 \][/tex]

8.

**Calculate [tex]\( 6 \cdot 1 \)[/tex]:**

[tex]\[ 6 \cdot 1 = 6 \][/tex]

Therefore, the value of the algebraic expression [tex]\( 6x(y^2z) \)[/tex] with the given values for [tex]\( x \)[/tex], [tex]\( y \)[/tex], and [tex]\( z \)[/tex] is [tex]\( 6 \)[/tex].

So, the correct answer is:

D. [tex]\( 6 \)[/tex]