To find the fourth proportional to the numbers \(2 : 8 : 3 : x\), we use the concept of proportionality. In this case, \(2\), \(8\), \(3\), and \(x\) are in proportion, so we can write:

\[
\frac{2}{8} = \frac{3}{x}
\]

To solve for \(x\), cross-multiply:

\[
2 \cdot x = 8 \cdot 3
\]

This simplifies to:

\[
2x = 24
\]

Now, divide both sides by \(2\):

\[
x = \frac{24}{2} = 12
\]

Thus, the fourth proportional is:

\[
\boxed{12}
\]

Would you like further details or have any questions?

Here are some related questions for additional practice:
1. Find the fourth proportional to \(5 : 15 : 10 : x\).
2. If \(3 : 12 : 4 : x\), find the value of \(x\).
3. What is the fourth proportional to \(7 : 21 : 14 : x\)?
4. Calculate the fourth proportional to \(6 : 18 : 8 : x\).
5. If \(9 : 27 : 3 : x\), determine the value of \(x\).

**Tip:** In a proportional relationship \(a : b = c : d\), cross-multiplying (\(a \cdot d = b \cdot c\)) is a quick way to solve for the unknown term.

Learn how to find the fourth proportional in a given ratio with this example: 2:8:3. This step-by-step solution explains the concept of proportionality and demonstrates the cross-multiplication technique used to determine the missing term in the ratio. Ideal for students in Grades 6-8.

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