which parts are you not having update?
The Needed Qty is set to be WO::wo_qty * blin_quantity
But the fields on your portal row are BOM_LINES::wo_quantitiy and WO::wo_quantity
I see a number of issues. For start, Since "Allow Creation of Record via this relationship" is not enabled for the relationship between WO and BOM_lines, you cannot create new records directly in this portal and you don't seem to have any other method in place for adding lines to this portal.
With "Allow creation..." enabled, I still cannot add new items to the list as the field in the Item column is a calculation field instead of a data field and behavior settings in the inspector deny access. After I clear those, I find that "do not modify" has been specified on the field and I have to remove that option.
The errors and roadblocks keep popping up up from there...
You may want to examine this simple invoiceing demo (Created by Comment), and just think of an Invoice as your WO table: http://fmforums.com/forum/showpost.php?post/309136/
I tried creating another layout to look at the BOM_LINES data and the WO::wo_qty is empty for every BOM_LINES record, suggesting that there is something not right in that relationship.
It seems that if you are going to have work orders that pull materials from the BOM table through the BOM_LINES, the WO and BOM_LINES should be related by wo_number-id rather than bom_number_id (along with the "allow creation of records via" that Phil indicated)
Also you may want to change your id fields to be auto entered number fields rather than text fields.