What is the definition of the 4th state of matter?

The most familiar examples of states of matter are solids, liquids, and gases; the most common state of matter in the universe is plasma. Less familiar phases include: quark-gluon plasma; Bose-Einstein condensates and fermionic condensates; strange matter; superfluids and supersolids, and possibly string-net liquids.

They aren't really numbered, so which one is the 4th is really not defined. Your teacher is probably looking for Plasma.

If you want some more info on "plasma," check out:

Plasma (physics) - Wikipedia, the free encyclopedia

It might give you a definition of what plasma is.

Where I work, we use Argon gas, an RF (radiofrequency) generator, and a spark to generate plasma. Electrons get knocked off, and the Ar becomes Ar+. Ionized matter.