like the previous NUC8i3BEH it can support 12V-19V input by battery. i want to know are the NUC10i3FNH the same with this.-
No, the FN NUCs require 19V input and source must support 10A power-on surge. I might suggest you consider using a DC-DC "Buck" Converter to ensure a smooth 19V supply. Here is one you could consider: https://www.mini-box.com/DCDC-NUC. You can use your 16.8V battery with this converter.
It's pedantic, but technically that's a buck-boost converter, not a buck converter (buck = reduce voltage, boost = increase voltage, buck-boost = either/or). FWIW I love mini-box, I built a beastly little router using their stuff, lasted us 8+ years and was still going strong except I needed AES-NI support as pfSense started requiring it, and the old Atom processor didn't have that.
I do concur that attempting to run a 10th gen NUC directly off of a 16.8V power supply will probably result in a lot more headaches than it's worth. It might work... but you might have system instability or other transient/intermittent issues that will be a nightmare.
Also, the battery would need to be capable of supplying at least 6.42 amps, as the 10i3 has a 90W power supply, and when you consider a 80-90% efficiency on the converter:
90W / 16.8V = 5.35A (direct power requirement of the NUC)
5.35A * 20% = 1.07A (power loss from the converter)
1.07A + 5.35A = 6.42A (total current draw the converter needs from the battery)