This is not the exact format George Berkeley put it in, but this is the basic idea.
1) The concept of matter is (among other things) the concept of a mind-independent material
2) If this concept is coherent, it should be possible to imagine a material object no-one is aware of
3) But it is impossible to imagine a material object that no-one is aware of, because if you visualize it you become aware of it.
4) The concept of matter is incoherent
5) Matter cannot exist.
Remember, he's not trying to mess with your head. He's just looking for the truth. The 'solution' is (A) that he is confusing the symbol for what it is symbolizing--by imagining a unicorn I do not become aware of any unicorn. I mearly have a representation of what one might look like. And (B) there is a difference between an object and a class of objects. When thinking of a bit of matter that no-one is aware of, the bit of matter I come up with might not look like any real piece of matter. It does (I hope) look pretty much like the average piece of unknown matter.