tl;dr: If you do not need the audio channel, do not buy Type C to HDMI dongles, buy Type C to DisplayPort.
I purchased a LG 27UD68 27" 4k display to work on at home. Since my Pixelbook only features 2 USB Type C ports, I was in need of a dongle to get it to extend the desktop to the display or to work in clamshell mode. I tried 2 Type C to HDMI dongles and they all had major issues. One only handled 4K at 30Hz while the other had annoying connection issues that caused the display to fade to black every 2-3 minutes.
I now purchased at Type C to Display Port dongle that works without issues. It seems that the HDMI dongles don’t have the computational juice to handle the bandwidth required to drive such a resolution. According to the reviews of both HDMI dongles, they’re both hit or miss, both they where advertised as being compatible with the Chromebook Pixel, so I gave them a chance.
If you don’t want to risk it and your display supports DisplayPort 2.1 (which any 4k display probably will), buy this dongle* on Amazon.
_* This is not an affiliate link._