Based upon the number of carbon atoms attached to a carbon atom, it is termed as primary (1°), secondary (2°), tertiary (3°) or quaternary (4°) . A tertiary (3°) carbon is attached to three other carbon atoms.

Let us evaluate the structures of the given isomers of $\text{C}_6\text{H}_{14}$:

1. 2-Methylpentane ($\text{CH}_3\text{-CH(CH}_3\text{)-CH}_2\text{-CH}_2\text{-CH}_3$): The C-2 atom is attached to three carbons, so it has exactly one 3° carbon.
2. 2,3-Dimethylbutane ($\text{CH}_3\text{-CH(CH}_3\text{)-CH(CH}_3\text{)-CH}_3$): Both the C-2 and C-3 atoms are attached to three other carbon atoms . Thus, it contains two 3° carbons.
3. 2,2-Dimethylbutane ($\text{CH}_3\text{-C(CH}_3)_2\text{-CH}_2\text{-CH}_3$): The C-2 atom is attached to four carbons, making it a quaternary (4°) carbon . It contains zero 3° carbons.
4. n-Hexane ($\text{CH}_3\text{-CH}_2\text{-CH}_2\text{-CH}_2\text{-CH}_2\text{-CH}_3$): This is a continuous straight-chain alkane containing only primary (1°) and secondary (2°) carbon atoms .

Therefore, 2,3-Dimethylbutane is the correct compound.