Take your gloves before shaking someone's hand.

The correct option is Off.

To understand why "Off" is the correct choice, let's look at the phrasal verbs and vocabulary used in the sentence:
The sentence structure is: "Take your gloves ______ before shaking someone's hand."
We need to find the correct preposition/adverb that combines with the verb "take" to form a phrasal verb meaning "to remove clothing or accessories from the body".

Let's analyze the options:
1. take on: This means to accept a job, responsibility, or challenge (e.g., "take on a new project"). It can also mean to employ someone. It does not mean to remove something.
2. take in: This means to absorb, understand, or receive someone/something (e.g., "take in the view" or "take in a guest"). It can also mean to make clothing tighter.
3. take off: This is a common phrasal verb that means to remove clothing, accessories, or gear from one's body (e.g., "take off your shoes", "take off your hat", or "take off your gloves").
4. take with: This is not a standard phrasal verb; "with" is just a preposition indicating accompaniment (e.g., "take your umbrella with you").

Shaking someone's hand is a social interaction where it is polite to remove your gloves. Therefore, the action required is the removal of the gloves. The phrasal verb that means "to remove (an item of clothing or gloves)" is "take off".

Putting it together: "Take your gloves off before shaking someone's hand."