Translation:František and Matěj are her uncles.
Strýček is a diminutive. Strýc will be more likely found in official documents or statements about some family relationships. It is more common in the speech of some Moravian dialects.
In spoken word the most common is "strejda" but the "ý" -> "ej" is a sign of Common Czech, not Standard Czech.
You can check this comparison http://syd.korpus.cz/QI7SCGxU.syn Some of those words have some specific meanings or are used in some specific situations, like the "strejc" or "strejček", even without meaning a relative.
I was in doubt about the Strýcové (typing what i hear in Czech exercise). So I clicked 'discussion' because on top here I can see the correct Czech answer. Just like Mel32329 commented: in these type of exercises I only get the translated answer in English, not the answer in Czech that I had to type. So I cannot see if I made any typo's/small mistakes in spelling. That is a learning-moment lost! Can it not be programmed that together with the correct English translation you also see the correct Czech sentence, so you can compare? Would be very helpful!