Answer :

Let's solve the function \( y = 3x^4 - 2x^2 + 8 \) step by step for a specific value of \( x \).

### Step-by-Step Solution:

1. Identify the function:
\( y = 3x^4 - 2x^2 + 8 \)

2. Choose a value for \( x \):
Let's take \( x = 2 \) as our example value.

3. Substitute \( x = 2 \) into the function:
[tex]\[ y = 3(2)^4 - 2(2)^2 + 8 \][/tex]

4. Compute \( 2^4 \):
[tex]\[ 2^4 = 16 \][/tex]

5. Plug this back into the equation:
[tex]\[ y = 3 \cdot 16 - 2(2^2) + 8 \][/tex]

6. Compute \( 3 \cdot 16 \):
[tex]\[ 3 \cdot 16 = 48 \][/tex]

7. Compute \( 2^2 \):
[tex]\[ 2^2 = 4 \][/tex]

8. Compute \( 2 \cdot 4 \):
[tex]\[ 2 \cdot 4 = 8 \][/tex]

9. Substitute these values back into the function:
[tex]\[ y = 48 - 8 + 8 \][/tex]

10. Simplify the expression:
[tex]\[ y = 48 - 8 + 8 = 48 \][/tex]

So, for \( x = 2 \), the value of the function \( y = 3x^4 - 2x^2 + 8 \) is \( y = 48 \).

Therefore, the result is
[tex]\[ y = 48 \][/tex]