Take your gloves _____ before shaking someone's hand.

The correct answer is Option (3) → Off

A phrasal verb is a verb joined with a small word such as up, out or together. The two words together have a new meaning.

To take off a piece of clothing is to remove it. Good manners require removing one's gloves before shaking hands, so "Take your gloves off" is right.
Example: Please take off your shoes before entering the temple.

Complete sentence: Take your gloves off before shaking someone's hand.

Why the Other Options are Incorrect?

Option 1: On — Incorrect. To take on is to accept work or responsibility. For clothing the phrase is put on, which means to wear, the opposite of what the sentence needs.
Example: She took on the extra work without complaint.

Option 2: In — Incorrect. To take in a garment is to make it narrower. The phrasal verb also means to deceive someone.
Example: The old man was taken in by the fake salesman.

Option 4: With — Incorrect. "Take with" means to carry something along. "Take your gloves with" before shaking hands makes no sense.
Example: Take an umbrella with you.