**Explanation:**

**Degree of freedom** is a concept in statistical mechanics that refers to the number of independent ways a system can store energy. In the case of molecules, it refers to the number of ways the molecule can move and store energy.

A **linear triatomic gas molecule** is one in which the atoms are arranged in a straight line. Examples of linear triatomic molecules include carbon dioxide (CO2) and carbon monoxide (CO).

On the other hand, a **non-linear triatomic gas molecule** is one in which the atoms are not arranged in a straight line. Examples of non-linear triatomic molecules include water (H2O) and ammonia (NH3).

The number of degrees of freedom for a non-linear triatomic gas molecule can be calculated using the formula:

**f = 3N - R**

Where:
- **f** is the number of degrees of freedom
- **N** is the number of atoms in the molecule (3 for a triatomic molecule)
- **R** is the number of constraints on the molecule's motion

For a non-linear triatomic gas molecule, there are three atoms (N = 3) and no constraints on the molecule's motion (R = 0). Therefore, the number of degrees of freedom is:

**f = 3(3) - 0 = 9 - 0 = 6**

So, the correct answer is **six (b)**, which means a non-linear triatomic gas molecule has six degrees of freedom.