There are $2^6$ possible outcomes, one for each sequences of six heads-or-tails.
a. How many sequences of six tosses have all heads? One. Since there is one good outcome and $2^6$ possible outcomes, then the probability is $\frac{1}{2^6}.$
b. How many sequences of six tosses have exactly one head? Six (pick which toss is heads). So the probability of getting exactly one head is...
c. How many possible sequences have exactly two heads? Pick the two tosses that are heads; then you get...
d. An even number of heads means either no heads, two heads, four heads, or six heads. There is one sequence with no heads, one sequences with six heads, then xxx
sequences with two heads, and yyy
sequences with four heads. So the total number of "good" outcomes is $1+1+$xxx
$+$yyy
. So the probability is...
e. At least four heads... that means either no tails, one tail, or two tails. You already figured each of those in (a), (b), and (c) (well, for heads, but you can see that it's the same answer if you want to know the probability of "exactly one head" and the probability of "exactly one tail", right?). So...