Does one start with the right or with the elder when entering a gathering?

Question:
If a person enters a gathering and there is an elder present—whether a scholar or an elder in age—does he start with the right?

Answer:
He reaches the head of the gathering first and greets him, then whoever is on his right.
Q: And if he wants to offer something, such as coffee?
A: He starts with the head of the gathering, then whoever is on his right, just as they used to start with the Prophet (peace and blessings be upon him), then whoever was on his right.