unions are listed in the mysql manual under "Things that have to be done sometime" & "Things that must be done in the real near future" so draw your own conclusion about the support UNIONs have under mysql.
i'd either rewrite the query or execute 4 different queries.
heres a dirty little sql hack:
select count(t1.proj_type) as count1, count(t2.proj_type) as count2, count(t3.proj_type) as count3, count(t4.proj_type) as count4 from projects t1, projects t2, projects t3, projects t4 where t1.proj_type = '1' and t2.proj_type = '2' and t3.proj_type = '3' and t4.proj_type = '4'
i don't think the syntax is correct, but the basic idea is to alias the table names and apply the count() & where on the aliases.