I am not quite sure which Honda HRX you have, because I can not see the throttle control area of the mower in your pictures as close as I would need to. I will let Robert@Honda find that out for you (probably on Monday). But I DO know that the difference between the HRX217HYA and the HRX217HXA (no longer made) is that the HYA has auto-choke and the HXA does not. They both have the blade brake clutch.
Click on the links in the next to paragraphs for photos.
If the throttle control area looks like
THIS it should be the HXA. Notice the choke is not automatic and after you start it you have to switch it into the fast postion.
And if it looks like
THIS it should be the HYA. Notice how there is no CHOKE setting on the throttle. You put it in the fast position to start it AND to mow.
Robert@Honda should be able to determine what mower you have, so check back for a reply. But I hope my info helped you learn the difference between the HYA and HXA. :smile: