Praise be to Allah.
This is an issue which some people do not understand. When you meet someone or you enter upon someone and you want to greet them (by shaking hands) or by offering tea or coffee, then you should start with the oldest, because the Prophet (peace and blessings of Allaah be upon him) had a miswaak (tooth-stick) in his hand and there were two men in front of him. The younger man wanted to take it, but he said to him, “The older, the older.”
This is different to when there is a young man on one’s right and an old man on one’s left, and one is sitting between them. In that case one should start on the right, even though that man is younger.
On this basis, when a person enters a gathering, he should start with the oldest, but if he wants to give something, then he should start with whoever is on his right, not on the right of the oldest.