can i install 2400mhz ram on my gigabyte h170 d3h?

Your CPU supports memory up to DDR4-2133. Anything above this is overclocking the memory controller on the CPU, although most should handle DDR4-2400 with XMP profile settings.
The website for your motherboard doesn't list XMP support, and only lists support for DDR4-2133 memory, so it seems they really didn't have overclocking in mind for this board.
It won't hurt to get the memory anyway. It will work at DDR4-2133 speed out of the box, and you can then check the BIOS settings to see if you can increase this to DDR4-2400.
 


Yeah should be fine. You motherboard doesn't support overclocking RAM so you wont get the benefit of the 2400 speed, but it should auto set the speed to the default of 2133. For simplicity sake its always best to get the right speed RAM for your motherboard but if there's a good sale on the 2400 stuff it makes sense.