焼（や）き is a noun form of the verb, 焼（や）く = to grill and 餅（もち） is a rice cake. So 焼き餅 is what is shown in the picture, a grilled rice cake. Plain 餅（もち） in Japan is made of glutenous rice, so when it’s heated, it gets really stretchy and sticky. Unfortunately every year a number of people die of choking while eating 餅（もち）. So 夫の焼き餅に困っている can mean that “I am having a hard time dealing with my husband grilled rice cake.”
However, 焼き餅 has another meaning, which is “jealousy” or “envy.” So 夫の焼き餅に困っている more likely means: “I don’t know what to do with my husband’s jealousy.”
to be jealousy can be described as 焼（や）き餅（もち）を焼（や）く
a jealous person can be called 焼（や）き餅（もち）焼（や）き
