How can I find a person on Facebook or any other social site by his last name and photograph

You don't by a photograph... and you can spend a very long time looking by a last name, because you woudl have to go throuh EVERY person with an account with that same last name. And odds are you won't be able to see much if anything they have unless they friend you. And thats assuming they are even on it to begin with, many people aren't.

Seems kind of creepy trying to find someone by a last name and photograph. Why is this so important? Its obvious they don't know you because you don't know them.

He knows me we met before but unfortunately I don't have his number and other information please help me

There is nothing I or anyone else can do... you have search using his last name, Obviously you can discard people living in the wrong country, but there is no easier way to do it. But you are going to have a very hard time probibly not knowing his first name. Even with a first and last name you are likely going to find a LOT of people.. and as I said. Its possible none will be him as most people don't have Facebook accounts. And many smart people have their information restricted from being accessed by anyone who is not currently a friend.