Across two periods, there are four possibilities:

U, U end value: $96.80,
U, D end value: $79.20,
D, U end value: $79.20,
D, D end value: $64.80,
where U is an up move and D is a down move.
The probability of an up move followed by a down move is 0.75 × 0.25 = 0.1875.
The probability of a down move followed by an up move is 0.25 × 0.75 = 0.1875.
Both of these sequences result in an end value of $79.20.
Therefore, the probability of an end value of $79.20 is (0.1875 + 0.1875) = 0.375 = 37.5%. Alternatively, the following formula could be used:

where
n = 2 (number of periods)
x = 1 (number of up moves: ud and du)
p = 0.75 (probability of an up move)