But this is a religious issue with me. As long as the RDBMS supports it, you should use ANSI 92 join syntax. And you should use table aliasing as well.
So your query ought to be written as
from supplier_table as st join supplier_item_xref as six
on st.id = six.supplier_id
join item_table as it on six.item_id = it.id
where it.item in ('screw', 'stereo');
This allows the SQL optimizer to do a better job and can result is faster code for complex joins.
If your RDBMS doesn't support this, upgrade. It makes your code more readable.
I'm not wearing any pants