2004 leaking brake booster
The brake booster is only connected to the in take via a vacuum line, so if it is leaking replace it, parts stores will carry the line you need and clamps if you need them.
Leaking vacuum or fluid?
None of the hoses leak it leaks right where me finger points
Master cylinder has went bad, replace it quickly or you could ruin the booster also, if it hasn't done so already.
Tennisshoes is correct. The master cylinder is bad and leaking out the back. If fluid starts getting into the booster you will have to replace it also.
How can you tell if the booster has been compromised?
Pull the vacuum hose right at the booster and see if there is fluid traces in the hose or even the check valve, things should be dry in that area.
My system seems to be hydraulic
After expanding the pic you sent it is a hydro boost system so you won't have a vacuum brake booster.
Looking for a Used Suburban in your area?
CarGurus has 19,720 nationwide Suburban listings starting at $2,000.
Search Chevrolet Suburban Questions
Chevrolet Suburban Experts
Related Models For Sale
Used Cars For Sale