**Proof:**

To prove that f(x) * f(1-x) = 1 for all x ∈ ℝ, we can substitute the given function f(x) = 4^x / (4^x + 2) into the equation and simplify both sides.

**Substituting f(x):**

Let's substitute the given function f(x) = 4^x / (4^x + 2) into the equation f(x) * f(1-x) = 1:

f(x) * f(1-x) = (4^x / (4^x + 2)) * (4^(1-x) / (4^(1-x) + 2))

**Simplifying the numerator:**

We can simplify the numerator by multiplying the two terms:

4^x * 4^(1-x) = 4^(x + 1 - x) = 4^1 = 4

**Simplifying the denominator:**

Similarly, we can simplify the denominator by multiplying the two terms:

(4^x + 2) * (4^(1-x) + 2) = (4^x * 4^(1-x)) + 2 * (4^x + 4^(1-x)) + 4

= 4 + 2 * (4^x + 4^(1-x)) + 4

= 8 + 2 * (4^x + 4^(1-x))

**Final Simplification:**

Now, let's substitute the simplified numerator and denominator back into the equation:

f(x) * f(1-x) = (4) / (8 + 2 * (4^x + 4^(1-x)))

= 4 / (8 + 2 * (4^x + 4 - 4^x))

= 4 / (8 + 2 * 4)

= 4 / (8 + 8)

= 4 / 16

= 1/4

Since 1/4 is not equal to 1, we can conclude that f(x) * f(1-x) ≠ 1 for all x ∈ ℝ.

Therefore, the statement "f(x) * f(1-x) = 1" is not true based on the given function f(x) = 4^x / (4^x + 2).