Explanation:

- The concept of the fourth proportional is based on proportion relationships.

- For numbers a, b, and c, the fourth proportional x satisfies: a:b = c:x.

- Substitute given values: 48:72 = 108:x.

- Cross-multiply to find x: 48x = 72 * 108.

- Calculate the result: 48x = 7776.

- Solve for x by dividing: x = 7776/48.

- Simplify to find x: x = 162.

Option Analysis:

- Option 1: 72 - doesn't fit equation 48:72 = 108:72.

- Option 2: 144 - doesn't solve 48:72 = 108:144.

- Option 3: 120 - doesn't satisfy 48:72 = 108:120.

- Option 4: 162 - correctly solves the proportion.

.