From clause query

select count(*) 
      ,sum(case when dy in ('sat','sun') then 1 end) weekends 
from (       
   select to_char(trunc(sysdate,'yy')+rownum-1,'dy') dy 
   from dual 
   connect by level <= 365 
)

With clause

with years as ( 
   select to_char(trunc(sysdate,'yy')+rownum-1,'dy') dy 
   from dual 
   connect by level <= 365 
) 
select count(*) 
      ,sum(case when dy in ('sat','sun') then 1 end) weekends 
from years

livesql.oracle.com bug

select * from ( -- needed for bug in livesql.oracle.com
with years as ( 
   select to_char(trunc(sysdate,'yy')+rownum-1,'dy') dy 
   from dual 
   connect by level <= 365 
) 
select count(*) 
      ,sum(case when dy in ('sat','sun') then 1 end) weekends 
from years 
)