Sounds like flooding from a stuck float. Try managemyhome for an owners manual or maybe just contact honda.com.

Shut the fuel valve off-
Remove spark plug & ground the lead.
Pull the rope a few times and "blow" the excess gas out of the combustion chamber. (you don't want spark)
Reinstall plug and see if it ties to fire.

http://powerequipment.honda.com/support/owners-manuals/lawn-mowers/hrx

I just received a bit of news regarding my Honda mower. There person who gave it to me said that the previous owner had used high octane gas in the mower. After that it would not start or had difficulty starting it but Honda states to use 86 octane or higher so I wonder if the higher octane caused problems.
I am getting ready to take the air filter and carburator off to work on it. Thanks to all who have helped so far.

The octane would not cause the leak, although gas not treated with an "additive" and/or gas that had been stored too long might have caused the engine not to fire. This could in turn have led to flooding. Best Wishes--Carl Atlanta GA

I am in the process of trying to remove the carburator and having a challenge removing the fuel line. The clip is hard to pinch but I think once I can get pass that I will be able to remove the entire carburator to work on it. Lots of fun! :-p

use some wd-40 or other brands of slickem to remove stuborn hoses and bolts. I would try tomplum cleaning method with carb. spray can cleaner untilizing the instructions and cautions on the can first before tearing the carb. off. Not uncommon problem for equipment thats been setting or neglected for few months or years.

In my opinion, your first priority should be to see
EXACTLY where the fuel is leaking from. It could
be something as simple as a cracked fuel line, or
it could indeed be a stuck float in the carb.
Use mirrors, or disassemble the cowl,or whatever
it takes to see the origin of the leaking gas.
Then go from there.

Hi Mr. Plafolette,

I think your leaking petrol issue may be a cracked fuel tank. American Honda Motor issued a recall on the HRX217HXA models. Which I think is the one you have.

Affected Serial Numbers
MAGA - 1400001 ~ 1453724

More info is:

What is the problem?
Due to a manufacturing defect, over time, a crack may form in the fuel tank mounting tab causing a fuel
leak.
What should you do?
We strongly recommend that you stop using your lawn mower until the fuel tank has been replaced. If
you need assistance, please see a member of this dealership�s staff or any authorized Honda Power
Equipment dealer for assistance. If you need additional assistance that this dealer is unable to provide,
you may contact American Honda Customer Relations at (888) 888-3139.
In cooperation with the Consumer Product Safety Commission and California Air Resources Board

Recomend you stop using this mower until you can get it checked over.

Best, Mike.

Here is a link that might be useful: Safety recall link

Octane didn't cause the leak. If its not running and there is fuel leaking I'd say that the fuel hose from the gray shutoff to the carb is damaged. But who knows what the previous owner did to it.

If you need a new carb planopowerequipment.com sells them for ~$16 plus shipping for a complete carb.