Complete the polite host's question to her shivering guest.

"You look absolutely freezing! _____ a cup of hot chocolate to warm up?"

The correct answer is Would you like.

We use Would you like...? to make polite offers.

Be careful not to confuse this with "Do you like...?", which asks about a person's general preferences (e.g., "Do you like hot chocolate in general?"). Here, the host is offering a specific cup right now!