**Explanation:**

The favored conformation of a molecule depends on the stability of the different conformations. In the case of 1,2-dichloroethane and 1,2-ethanediol, the favored conformations are as follows:

**1,2-Dichloroethane:**
- 1,2-Dichloroethane is a molecule with two chlorine atoms attached to a central carbon atom.
- The molecule can have two possible conformations: gauche and anti.
- In the gauche conformation, the two chlorine atoms are in a staggered arrangement with a dihedral angle of approximately 60 degrees.
- In the anti conformation, the two chlorine atoms are in a fully staggered arrangement with a dihedral angle of 180 degrees.
- The anti conformation is more stable than the gauche conformation due to steric repulsion between the chlorine atoms in the gauche conformation.
- Therefore, the favored conformation for 1,2-dichloroethane is anti.

**1,2-Ethanediol:**
- 1,2-Ethanediol is a molecule with two hydroxyl groups (-OH) attached to a central carbon atom.
- The molecule can also have two possible conformations: gauche and anti.
- In the gauche conformation, the two hydroxyl groups are in a staggered arrangement with a dihedral angle of approximately 60 degrees.
- In the anti conformation, the two hydroxyl groups are in a fully staggered arrangement with a dihedral angle of 180 degrees.
- The anti conformation is more stable than the gauche conformation due to steric repulsion between the hydroxyl groups in the gauche conformation.
- Therefore, the favored conformation for 1,2-ethanediol is anti.

**Conclusion:**
- The favored conformation for 1,2-dichloroethane is anti.
- The favored conformation for 1,2-ethanediol is anti.
- Therefore, the correct answer is option 'C': Ant i, gauche.