How do I negotiate with a car dealer when I have a preapproved loan from my bank (Navy Fed Credit Union)?

So I'm on the hunt for a car, which will be a used one, and I went to Navy Fed and got preapproved for 12,000 BUT I only want to use at most 8,000 of it for a decent car (so my monthly payment won't be too high). So how do I negotiate with a car dealer to get the maximum savin gas on my behalf? For example, I'm looking at an 07 Honda Accord Ex-l listed at 8900. Can I treat my auto loan check as cash and claim I can give them 8000 for it? Can I used what I have saved up (2,000 cash) + 6,000 dollars worth of my loan check to take the car?
Thank you in advance!

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