At a bakery, cakes are sold every day for a certain number of days. If

Since 20% = 1/5 and 75% = 3/4, let the total number of days = the LCM of the two denominators = 20.
For the average number of cakes per day to be less than 4, the total number of cakes sold must be less than the following value:
20*4 = 80
Question stem, rephrased:
Were fewer than 80 cakes sold?

Since 6 cakes or more are sold on 20% of the 20 days -- implying that on each of these 4 days an INFINITE number of cakes can be sold -- it is clearly possible that 80 or more cakes are sold.
In this case, the answer to the blue question will be NO.

Statement 1:
The following distribution is implied:
20% of all 20 days = 4 days --> average of 6 or more per day
75% of the remaining 16 days = 12 days --> average of fewer than 4 per day
Remaining 4 days --> average of 4 or 5 per day

Minimum possible total for all 20 days = (4*6) + (12*0) + (4*4) = 40
In this case, the answer to the blue question will be YES.
Since the answer can be NO (as shown above) or YES (as shown here), Statement 1 is INSUFFICIENT.

Statement 2:
Examine the green values implied by Statement 1:
4 days --> average of 6 or more per day
4 days --> average of 4 or 5 per day
12 days --> average of less than 4 per day
Of the 8 days on which 4 or more cakes are sold, 50% have sales of 6 or more per day.
Implication:
Statement 2 implies the same distribution as Statement 1.

Thus, even when the statements are combined, the answer to the blue question can be NO or YES.
INSUFFICIENT.