When it comes to mixing prints, the most important things to consider are color palette, scale, and motif. Pay attention to how the scale of both patterns affect the look. Try mixing floral with animal print or a bold plaid. Stripes are another fun option. They play nicely when paired with a more organic print, and are very successful in monochromatic stories.
I don’t like to set hard and fast rules, but if you're looking for a safety net, consider this rule of thumb: let one print be the star. Choose your leading print and consider how to support with your remaining pieces. If your star is bright, don't go brighter. If your star is neutral, consider a monochromatic story and opt for a less eye-grabbing pattern in your supporting pieces.