The probability of Helena choosing n Phalaenopsis orchids is 0.25^n x (1-0.25)^(8-n) x 8Cn.
There's probably an 'nCr' button on your calculator.
Anyway, substituting 0, 1, 2 and 3 into that, the probability of her choosing:
• None is 0.100112915
• One is 0.266967773
• Two is 0.311462402
• Three is 0.207641602
The question tells us that she doesn't pick any more than 3, so these are the only possibilities available.
The probabilities that we are interested in are those of picking 2 and 3. Adding these gives 0.51904004. The total probability is 0.886184692, but as we know that there are no other possibilities available, we need to scale up the total probability to 1.
This is done by multiplying by 1/0.886184692, and doing the same to the probability that we're interested in gives 0.585774059, which when rounded to a sensible accuracy is 0.586.