Introduction:
In mathematics, proportions are used to compare two ratios or fractions. A proportion is an equation that states that two ratios are equal. It is often used to solve problems involving similar figures or calculating unknown values. In this question, we are given two terms of a proportion, 2.4 and 9.6, and we need to find the third term.

Given:
First term (a) = 2.4
Second term (b) = 9.6

Formula:
To find the third proportion, we can use the following formula:
a/b = b/x

Solution:
We can substitute the given values into the formula and solve for x:

2.4/9.6 = 9.6/x

Cross-multiplication:
To eliminate the fractions, we can cross-multiply and obtain:
2.4 * x = 9.6 * 9.6

Multiplication:
Performing the multiplication on both sides, we get:
2.4 * x = 92.16

Division:
To isolate x, we divide both sides by 2.4:
x = 92.16 / 2.4

Calculating the result:
Evaluating the division, we find:
x = 38.4

Answer:
Therefore, the third proportion to 2.4 and 9.6 is 38.4.