What type of column is 'birthday' ? The name implies that it should be a DATE column. If that's the case...
select name
from table
where sex='male'
AND MONTH(birthday) IN (1, 6, 12)
EDIT: I also assumed that you're using MySQL as your DBMS; if this isn't the case, then 'MONTH' might need to be changed to 'EXTRACT' (or some other equivalent date manipulation function) depending upon which DBMS you're actually using.