Which pattern of meter is used in this excerpt from "The Rime of the Ancient Mariner" by Samuel Taylor Coleridge?

It really depends on the excerpt that you have been given. Is this the one? I found in somewhere on the Internet.

The Bridegroom's doors are opened wide,

And I am next of kin;

The guests are met, the feast is set:

May'st hear the merry din.'

If this is the excerpt you have, then the answer is simple - alternating tetrameter and trimeter. Tetrameter means that there are 4 meters in one line, and given that one meter consists of two syllables, that would mean that there are 8 syllables in one line. Similarly, trimeter means that there are 3 meters, or 6 syllables in one line.