Solution:

To find the value of n, we need to solve the given equation n^np4 = 12 × ^np2.

Step 1: Simplify the equation

We can rewrite the equation as n^(n^4) = 12 × n^(n^2).

Step 2: Apply the exponential rule

According to the exponential rule, when the bases are the same, the exponents can be equated. Therefore, we can equate the exponents of n on both sides of the equation.

n^4 = n^2

Step 3: Solve the equation

To solve the equation n^4 = n^2, we can rearrange the terms to get:

n^4 - n^2 = 0

Factorizing the equation, we get:

n^2(n^2 - 1) = 0

This equation can be true if either n^2 = 0 or n^2 - 1 = 0.

Step 4: Solve for n^2

Case 1: n^2 = 0

If n^2 = 0, then n = 0.

Case 2: n^2 - 1 = 0

If n^2 - 1 = 0, then n^2 = 1.

Taking the square root of both sides, we get:

n = ±1

Step 5: Final solution

Therefore, the possible values of n are 0, 1, or -1.

In conclusion, the value of n can be 0, 1, or -1.