To solve the equation [tex]\(2 \sqrt{6x} = \sqrt{6x^2}\)[/tex], we will go through the following steps:
1. Square Both Sides: To rid ourselves of the square roots, we can square both sides of the equation.
[tex]\[
(2 \sqrt{6x})^2 = (\sqrt{6x^2})^2
\][/tex]
2. Simplify Both Sides: By simplifying, we get:
[tex]\[
4 \cdot 6x = 6x^2
\][/tex]
[tex]\[
24x = 6x^2
\][/tex]
3. Rearrange the Equation: Move all terms to one side to form a quadratic equation:
[tex]\[
6x^2 - 24x = 0
\][/tex]
4. Factor the Equation: Factor out the common term [tex]\(6x\)[/tex]:
[tex]\[
6x(x - 4) = 0
\][/tex]
5. Solve for [tex]\(x\)[/tex]: Set each factor to zero:
[tex]\[
6x = 0 \quad \text{or} \quad x - 4 = 0
\][/tex]
This gives us:
[tex]\[
x = 0 \quad \text{or} \quad x = 4
\][/tex]
So the possible values of [tex]\(x\)[/tex] are [tex]\(0\)[/tex] and [tex]\(4\)[/tex]. Out of these, we see that [tex]\(4\)[/tex] is listed among the provided answer choices.
Thus, one possible value of [tex]\(x\)[/tex] is [tex]\(4\)[/tex]. Therefore, the correct answer is:
(D) 4
