I need a derailleur hanger for a Schwinn S-25 dual suspension mountain bike. I don't have the hanger. Is there a part or model number for the hanger so that I can order a new one?

I had a look at the Mongoose website.
They have manual for download.

https://int.mongoose.com/pages/product-manuals

Enter the model of your bike, or look for a picture of it.
Follow the instructions....

REgards
Geoff

Below are Google searches related to selecting derailleur hangers and derailleurs:
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Rim may be bent, take bike to local bike shop

There is a good tutorial with photos here, How to Adjust Rear Bicycle Derailleur
most bikes are pretty similar, and there are a few vids on youtube you can search out. It's much easier to look at the tutorial than describe here, after all they've already done all the hard work!

I am assuming you are referring to the front derailleur. Here is a link to adjusting the front derailleur:
Park Tool Co ParkTool Blog Front Derailleur Adjustments

Take it to a bike shop for that. Labor is involved.

Web search things like "bent deraileur", "slipping chain" for an idea what the cause and solutions would be. Web search for the cost of 8-speed chains and rear derailleurs. The derailleur hanger itself could be bent. THAT is for a Bike Shop to deal with.

My guess is the total repair would be more than you paid for the bike but probably worth it.

Web search everything like "how to...". Lots of answers out there including videos.

http://bike-street.blogspot.com/2010/02/schwinn-mens-ditch-20-full-suspension.html

Take it to a search engine and get instant video answers.

"how to re install a derailleur"

You need to replace the main pivot bolt, something (most likely a tab) is broken. This one is best taken to your local bike shop for inspection. There may be something your missing like a crack in the body or another broken part. Link to Manual.

You can also contact the SRAM customer service for support, but they will refer you to a shop to take care of the problem and order any parts on this type of problem.

Hi

Trek's serial numbers are on the underside of the bottom bracket. Flip the bike over and read the letters and numbers. It will look like this :

9000697000480

This would be a Trek 9000, made in June 1997 and number 480 off the production line.

Hope this makes sense and you can decipher your bike. Vote for me if this helps, thanks.

You may have too large a tire on the back for the bike. However, if the derailleur hanger is bent, this could also cause the problem. Flip your bike over onto the bars and seat and make sure the derailleur alignment is good (vertically and longitudinally straight). If the derailleur hanger is straight, then you will have to use a narrower tire in the back.