I have a small walk in closet extending 6' into the garage attic from my master bedroom. The garage is 22' wide and I would like to extend the closet to a depth of 16' - 20'. The garage roof and ceiling is built with trusses. I want to add a laminated beam under the 2" x 4" ceiling joists across the width of the garage to carry the weight. What size beam do I need?

I am a bit confused on 2 points. Are you sure the ceiling rafters are 2x4 and how is this room going to extend through a space where a truss exists or am I missing your design idea.

I am not sure yet of the size of the ceiling rafters. There is already a room extending part of the way through where the truss was. I assume that the cross braces were moved, verticle braces were used as studs, and then additional cross braces were added out side the room.

I want to add a laminated beam under the 2" x 4" ceiling joists across the width of the garage to carry the weigh
Just to poke my nose in here if garage ceiling/ the new room floor is 2x4s then a beam isn't the issue yet it's the size of the floor joist which was designed to carry the roof.

Are the rafters/truss an ( A ) design with a collar beam? If the truss there is a ( W ) design or inverted ( W ) design and that is removed the complete deflection is changed on the loads.

Keep on Mind the bottom Cord of a ( W ) design inverted or not basically carries the top cord of the truss system.

Bottom line here by code or otherwise that area is for light duty storage at best and that's only if you have a 2x6 bottom cord or better. This sounds more like an addition going above that ceiling being 16' deep and 20' wide.

From my perspective as a builder this sounds like trouble. You need large enough dimensional lumber for a " floor" to exist and then a beam to help support that floor. I could see this going in and the house sold later and someone thinks it's a bedroom/game room etc

If your area was once all trusses and now some have been cut away some supports to make a room I think you are on thin ice already. An architect or engineer could give you a better opinion but I think every single truss must be left the exact way they were designed or you are going to carry the load properly.

Problem Solved. I went in the attic over the garage today and found that:

There are no trusses at all.
The ceiling/floor joists actually run in the opposite direction from what I previously thought.
There is a support that runs from front to back of the garage that looks like a wall.
The ceiling/floor joist are 2 x 12 on the side of the garage adjacent to the master bedroom.