Hi bobber, welcome to Outdoorking.
Let's start with the easy part. The serial number prefix GJ03 means that your engine is a GXV160, which is currently Honda's most popular push-mower engine. Furthermore, your particular engine was made in Japan, and may therefore have better quality control than the more common run of GXV160 engines, which are currently made in China.
With regard to the mower number, H means Honda, R means rotary mower, 21 means it has a 21" cutting width, and 6 means it has an engine of approximately 6 hp. The advertised horsepower of the GXV160 is actually 5.5, but because Honda only uses 3 digits to describe the mower dimensions, and "5" had already been used for their 5 hp engine (the GXV140), they chose to cheat a bit and call the GXV160 "6" in the model name. There should be a sticker on the top of the engine's plastic top cover, stating that it is 5.5 hp.
I'm not familiar with a trailing zero in a Honda mower model number: the next figure after the engine power, if there is one, usually designates series number, if we add a "K" in front of the number. AFAIK, there never was a series K0. It looks to me as if that is a European model, not covered by either the American or Australian model numbers, both of which I can more or less make sense out of (though they are different from each other). You may find out more by looking specifically at Honda's European sites.
If there is something wrong with the mower and you are looking for assistance with this, please let us know.
