10 years old?  Have you had it checked by a mechanic yet?  Way overpriced.

The car may well be OK if it's been well-maintained (a mechanic can determine that) but the price is insane.

Sure, it may be overpriced in a 'normal' market, but we are not living in a normal market world anymore. Gasoline is overpriced, but I see plenty of people buying gas everyday. In our current market 12,500 may be a decent price for this V6 Accord if it has been properly maintained according to the Honda recommended maintenance schedule. Things like: oil and filter changes, air filter, timing belt, spark plugs, transmission fluid, power steering and brake fluid flush, coolant flush, etc. Have all recalls been serviced? No accidents or flood damage? When was the last time the brake rotors and pads were replaced. How about the tires? You don't want to spend 12 five and then turn around and spend another thousand or more to update the maintenance.

Have you seen and driven the car? Is it clean inside, outside and underneath? Any leaks or exhaust smoke?

As @chucktobias stated, you would need to have it inspected by a qualified mechanic.