I know you can divide a signal into blocks in the frequency domain then process each block then add up the signal. But in your case, the signal xn is in time domain. The concept of of 8 blocks either means 8 independent filters or it means one filter of 1024 taps broken for implementation sake.
In case you have to pass one block of data into one delay pipe and not pass it through to other blocks in succession then your filter becomes actually 8 independant filters for same input but segragated sections. May be your professor wants then somehow to choose among them. Addition here breaks the meaning of filtering but can still be viewd as some sort of averaging if you add the 8 results in parallel. So overall I am not clear really just like you. Possibly modelling will help