Translation:Wash your hands before eating the strawberry cake.
~으세요 should probably be translated as "Please ~". It's kind of hard to translate imperatives in Korean because there are 3 basic levels whereas English just has 2 basic levels. 이거 해. Do this. (Impolite command) 이거 하세요. (Please) do this. (Polite command) 이거 해주세요. Please do this. Please do me a favor and do this. (Polite request) It really depends on context whether a ~으세요 command should be translated with 'please' or not. It wouldn't be correct to teach an English speaker that they all translate to not saying please (which can be rude in some contexts) and therefore the lowest level of politeness. If you look at the common contexts in which ~으세요 commands are used it maps much better on to "Please do" than just "Do". Please exit on the right. Please only take one. Please be quiet in the library. These are not commands that would use ~주세요 but just ~으세요.
From the notes
Generally speaking, a gerund is the ~ing form of a verb, a verbal noun. Korean has two ways of forming what would be a gerund in English, with overlapping but slightly different uses.
The most popular form is the present tense modifier (V는) plus 것. This form is the more common in speaking. 하는 것 has a connotation of an ongoing action, not just "doing" but "the act of doing." Just like in other circumstances, 것 can be abbreviated or contracted to 거, 건, 게, 걸.
The second form is made by taking the verb stem (V) plus 기. This form may sometimes be more formal. 하기 has a more general connotation, "doing," and may be more abstract or impersonal. To say "before doing X" we use this form, saying X하기 전에.
Since no part of a Korean meal is traditionally eaten by hand, it seems many Koreans might not have the habit of washing their hands before eating. On the other hand, there are restaurants in Korea where customers have to take off their shoes at the door. Blowing one's nose in front of other people is also considered impolite, so it's probably best to go to the bathroom for that.