You should be able to do
select to_number( to_char( request_time, 'HH24' ) ),
count(*)
from service_request
group by to_number( to_char( request_time, 'HH24' ) );
The to_number
is probably not strictly necessary but it makes more sense to return a numeric hour than a string hour for things like sorting.
If the data type is actually a timestamp, then you could improve this
select extract( hour from request_time ),
count(*)
from service_request
group by extract( hour from request_time );
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