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it depends which permissions you have in that space. There are two permissions for deleting attachments (delete own, delete attachments (all) ).
Head over to the attachments page, either by using the paper-clip icon to the right of the breadcrumb or by using (...) at the top right of the page and then select Attachments. Now check if there is a Delete link for the attachment you want to delete.
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February 28, 2019 edited
Exactly! Can you delete pages, for example? You just need the appropriate permission. Confluence is designed so anyone in an org can create content, but removing is an entirely different thing!