charge 5v battery with 12v solar panel
What you refer to as a "battery" is actually a USB power bank, and you must not attempt to charge it with 12V!

The only safe method of charging that USB power bank, is a power source electrically equivalent to a USB port i.e. well-regulated 5V (I will see if I can find the minimum current requirement - check the USB power bank user guide for that information).



Edited to add: Based on the user manual for that USB power bank, it takes up to 5hrs to recharge, and has a 2200mAh capacity internal battery. Therefore it is unlikely to attempt to draw more than the expected 500mA from the external power source (which could be a standard USB port) when recharging its internal battery.

You mentioned "4200mAh" in your question - a typo of 2200mAh perhaps, as it doesn't agree with the webpage you linked?



Also note that not all (in fact I suspect a minority of) USB power banks can be recharged at the same time as also "charging" (i.e. powering) their output device. I did not find any mention of that feature on the web page which you linked - if simultaneously being charged and powering the Raspberry Pi Zero, was actually your intention.