Can you sell an item if you give credit to the crochet pattern designer?

it depends on what is stated in the pattern. sometimes a designer will say make all you want for yourself, but do not sell your work to others.

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The designer (or publisher if rights were sold) holds copyright on his or her pattern. They decide what is done with the pattern. This applies to patterns you buy and patterns that are free. Some will give permissions on the pattern or on their web site. Others you may have to write and ask for permission. Still others may say they do not allow for profit sales using their patterns but may allow sales for charity efforts. Some will allow single sales, but not multiple sales. As noted above, it just depends. If in doubt, ask.

The pattern itself is never to be sold with an item or shared anywhere without permission from the designer.