I cant seem to figure out this formula

CycleWyze 

If you have access to the newly released GROUPBY function, it can make short work of this request.

=LET(
    avg_days, LAMBDA(arr,
        LET(
            k, ROWS(arr),
            sorted, SORT(arr),
            IF(k = 1, @arr, AVERAGE(DROP(sorted, 1) - DROP(sorted, -1)))
        )
    ),
    GROUPBY(Table1[Name], Table1[Date], avg_days)
)

First, 'avg_days' is created to be used with GROUPBY.  This function will take the date(s) being returned by GROUPBY and do some subtraction.  If only 1 date is found for a person, then the date is returned instead of the average. Sorting is done to ensure the dates being subtracted are in ascending order.

GROUPBY obtains a list of unique names from the table and takes in the date as the value -- the avg. days Lambda is applied to each return.