Q:

What is the largest number you can create with 0000 by moving only two sticks?

Here's what I'm saying

Moving 2 sticks, what is the largest number that you can create? 

A:

How about...

 Take the top and bottom sticks of the first zero, and place them upright on the bottom left, making $11^{11000}$?

If that's unrealistic...

... because the base is usually in bigger font, then $11000^{11}$ could work as well.

A:

How about:

 

As in,

 g900, the 900th term of the series used to generate Graham's number.

A:

Move the top and bottom matchsticks from the 3rd zero to make:

 

Where the first two characters are B's thus: BB110
And BB refers to the Busy Beaver Function
The Busy Beaver function is non-computable and therefor grows faster than any computable function such as exponentiation or the series to create Grahams Number. 
The first few entries:
BB2 = 6 
BB3 = 21
BB4 = 107   
BB5 ≥ 47,176,870
BB6 > 7.4 × 10^36534 which is already greater than greenturtle3141's answer
BB12 > g1 

which is already close enough to catching up to Graham's Sequence to pretty safely say that BB110 > g900 considering BB continues to ramp up faster than any computable function.

