find parts with two or more suppliers:
select part_id
from catalog
group by part_id
having count(part_id) >= 2
find the supplier(s) of those parts, more future-proof, can show two or more suppliers:
select c.part_id, s.supplier_name
from catalog c
join supplier s
where c.part_id in (
select part_id
from catalog
group by part_id
having count(part_id) >= 2)
order by c.part_id, s.supplier_name
but if you want parts which exactly has two suppliers only:
select c.part_id, group_concat(s.supplier_name) as suppliers
from catalog c
join supplier s using(supplier_id)
where part_id in (
select part_id
from catalog
group by part_id
having count(part_id) = 2)
group by c.part_id
if you want only those two suppliers to display in two columns.. me thinking too... :-)
[UPDATE]
what i thought up:
select c.part_id, c.min(c.supplier_id) as first, c.max(c.supplier_id) as second
from catalog c
join supplier s
where c.part_id in (
select part_id
from catalog
group by part_id
having count(part_id) = 2)
group by c.part_id
order by c.part_id
to get the supplier names:
select x.part_id, a.supplier_name, b.supplier_name from
(
select c.part_id, c.min(c.supplier_id) as first, c.max(c.supplier_id) as second
from catalog c
join supplier s
where c.part_id in (
select part_id
from catalog
group by part_id
having count(part_id) = 2)
group by c.part_id
order by c.part_id
) as x
join supplier a on x.first = a.sid
join supplier b on x.second = b.sid