Janetsflower has got the answers right but, since you still seem unable to explain it to your daughter, I'll have a go:
Q1: 2 out of 10 balls are red, so the probability of getting a red ball is 2/10. (That's 2 over 10, or two tenths. Writing fractions on AB is tricky!).
So you expect to get a red ball on two tenths of the occasions on which you select a ball from the bag. Since this is done 30 times, the expected number of red balls is two tenths of 30, and 2/10 x 30 = 6.
Q2. Everything is the same as before, except that a ball is only drawn out on only 15 occasions, so the sum becomes 2/10 x 15 =3.
NB: I strongly recommend that you check that you've read the questions correctly. It's rather unusual for a book (or a teacher) to effectively ask the same question twice (i.e. only the number of trials has changed). It would be more likely that, if the first question asks about the expected number of red balls, the second question would ask about the expected number of blue balls. (If you want blue balls, instead of red ones, just multiply by 8/10 instead of 2/10).
Chris
PS: It sounds like those questions were set by an inexperienced teacher. During 15 years of teaching maths, I learnt to talk about putting counters into a bag, never balls. Otherwise, sooner or later, you find yourself asking your class something like "What is the probability that I've got two blue balls? That is absolutely guaranteed to start any class giggling and it's almost certain that some wag will shout out "Doesn't that depend upon how cold it is, sir?" ;-)