To determine what value of [tex]\( x \)[/tex] makes the proportion [tex]\(\frac{x}{6} = \frac{36}{24}\)[/tex] true, we follow these steps:
1. Identify the proportion:
[tex]\[
\frac{x}{6} = \frac{36}{24}
\][/tex]
2. Cross-multiply to eliminate the fractions:
[tex]\[
x \cdot 24 = 36 \cdot 6
\][/tex]
3. Perform the multiplication on each side:
[tex]\[
x \cdot 24 = 216
\][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 24:
[tex]\[
x = \frac{216}{24}
\][/tex]
5. Simplify the division:
[tex]\[
x = 9
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] that makes the proportion true is [tex]\( \boxed{9} \)[/tex]. Thus, the correct answer is [tex]\( A \)[/tex].
