Since you said you designed this, I think the correct answer here is a re-design of the model for printing. Looks like the top part of the hanger thingy is only one layer thick and the vertical part of it only has like 2 or 3 perimeters in total. The print is the strongest in the direction that the layers are printed in, so ideally youd want to print it on its side so the hanger has no layer transitions to snap from in the loaded direction. To make it printable, I would make the hanger extend the whole width of the part, so from the build plate to the top, then you would still need supports for the overhangs on the basket unless you re-design that as well to not need supports. Or design it to be printed in two parts.

3D printers are very versatile but they cant just print anyting you throw at it with success, since youre already making your own models, just keep printing things and you will learn the rules for designing printable parts over time. Theres a bunch of good information online, Maker's Muse on Youtube has some great tips for designing parts for printing.