you cant issue a delete statement on two tables, since the delete statement here is issued on the join of the two tables not the tables themselves, so you are issuing a delete on a table that doesnt really exist in your database (rather than on a table that was created by the database software on the fly as the result of the join)
if you want to delete more than one row in more than one table then you should issue two delete statements like
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delete * from link where careerid in ( select id from careers2 where careername = 'administrative assistant')
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then
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delete * from career where careername = 'administrative assistant';
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how ever in your case, there is no need for all of this, you should simply make your careerid a primary key in the Career table linked to the id key in the Link table.
and in the relationship scheme (in database tools) make sure that the link between the Career and Link to have Reinforce Referencial Integrity and Cascade on Delete checked)
so! when you delete the master record the slave record will get deleted as well.
so you will end up with a simple delete statement of the form:
delete * from career where careername = 'administrative assistant';
and the linked records in link table will be cascade deleted.