there is a piece of photo paper stuck in my 6510 Hp printer?

Unfortunately there's very little you can do & very little access for the paper path in this printer. According to the manual:

To clear a paper jam

1. Open the cartridge access door.

2. Open the paper path cover.

3. Remove jammed paper.

4. Close the paper path cover.

5. Close the cartridge access door.

6. Try printing again.

Otherwise you'd have to get very creative or have someone who is very technical take a look at it to see what they could do. One trick I've sometimes used to clear out an obstruction that's hard to get to is to manually force a piece of card stock (like a file folder) cut to size to fit through the paper path, into and through the paper path to force out the problem, but you need to be careful & try to only push it through in the direction that the paper normally goes through to prevent other damage to sensors.

There should be a button you can press to make it try to eject. But if that doesn't work just try to pull it out.. I had to do that with my printer once, and it's perfectly fine now. Just make that the last alternative.

Check out this HP link pertaining to your 6510 paper jam problem