Find
the fourth proportional to 2a, 3b and 4c.

Answer

To find the fourth proportional to the numbers \(2a\), \(3b\), and \(4c\), we can use the property of proportions.

### Step-by-Step Solution:

1. **Define the Fourth Proportional**:
Let the fourth proportional be \(x\).

2. **Set Up the Proportion**:
According to the definition of fourth proportional, we have:
\[ \frac{2a}{3b} = \frac{4c}{x} \]

3. **Cross-Multiply**:
Cross-multiplying gives us:
\[ 2a \cdot x = 3b \cdot 4c \]

4. **Simplify the Equation**:
This simplifies to:
\[ 2ax = 12bc \]

5. **Solve for \(x\)**:
To isolate \(x\), divide both sides by \(2a\):
\[ x = \frac{12bc}{2a} \]

6. **Further Simplify**:
Simplifying the right-hand side gives:
\[ x = \frac{12bc}{2a} = \frac{6bc}{a} \]

### Final Answer:
Thus, the fourth proportional to \(2a\), \(3b\), and \(4c\) is:
\[ \boxed{\frac{6bc}{a}} \]