What would be the best way to ask for $8,000 to get A 3D printer + supplies to make a prototype of an invention I have?
Do you mean the best way to approach an investor about it, or the best group/person to approach about investing?
If the former I would say go through and show that you have clearly defined goals (what completion looks like, what information you are collecting) along with a clear timeline and action plan of what you will do once the prototyping phase is over. If the individual/group isn't familiar with your industry you may want to highlight or explain how common prototyping is (or how it is used when it is used.)
If the latter, then I would consider starting with the good ol' reliable 3 F's (Friends, Family, Fools.) I have worked with dozens of bootstrapped entrepreneurs and the vast majority of them raise money to get their new ventures going through people they know. It is typically the shortest path for getting the cash you need, and since most first rounds of financing are small relative to the rest of the rounds this may be the perfect time to hit up people who just care about and support what you do. Take my advice though and make sure the investment is formalized and documented and consider using either a straight equity option or if you want to give them some protection you can do a convertible or SAFE style document. If personal networks are out then I would consider crowdfunding or (like many people have done) take out a personal Credit Card and run it down from there. I would suggest that as only a last resort, but I've known many businesses that started with a CC application on a college campus or outside a convenience store (when they used to do that at least haha.)
I've worked with startups who launched with as little as a few thousand dollars from friends/family all the way to seed rounds/series rounds ranging from the hundreds of thousands to millions. If you'd like to discuss seed financing and prototype fundraising/best practices feel free to reach out and schedule a time to connect!