To find out how many more miles Hassan needs to ride to meet his goal of 26.8 miles, we first subtract the miles he has already ridden from his total goal:
\[ 26.8 \text{ miles (goal)} - 6 \text{ miles (already ridden)} = 20.8 \text{ miles (remaining)} \]
Next, we need to determine how many miles he needs to ride each day over the next 4 days to meet this remaining goal. We do this by dividing the remaining miles by the number of days:
\[ \frac{20.8 \text{ miles}}{4 \text{ days}} = 5.2 \text{ miles per day} \]
Therefore, the average number of miles Hassan would have to ride each day for the next 4 days is
\[ \boxed{5.2} \text{ miles per day}. \]
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