Gumducks are a type of collectible in Biomutant that are tied to the achievement / trophy "Quack" where you need to collect a total of 20 gumducks. These collectibles are first found during the quest from Goop in the Surfipelago region where he will ask you to find 6 gumducks for him.
This is the only quest where you collect gumducks, so you need to find the remaining 14 on your own if you want the achievement or trophy. So, how do you find more gumducks in Biomutant?
Gumducks are only found in Quack Hollow in the Surfipelago region. This is the same area where your found the 6 for the original quest. They will respawn about 30 minutes after you collect them for the quest, and thereafter roughly every 30 minutes. So return to Quack Hollow every 30 - 40 minutes to collect another 6 gumducks until you have them all.
There can only spawn 6 gumducks at a time, so you do need to return there for a total of 4 times in total to get all 20 needed for the trophy or achievement. Luckily getting there is fast and easy, and just fast travel to Goop and surf north to go in there. Each trip should only take a few minutes.
Keep in mind that the gumducks only spawn if you are playing, so the 30 minute timer is in-game time. So you can't just collect the 6 gumducks, turn off your game and return after 30 minutes. Instead you must leave the game running for the duration of the time.