To call data from the adoptables table (or any table), you would just use a line of code likes this:
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$mysidia->db->select("adoptable", array("Column"), "Row = '$somevalue'")->fetchColumn();
With "adoptable" being the table name. It is case-sensitive though, so it must be exactly how it is typed in phpMyAdmin. Just change adoptable to owned_adoptables if you want that table.
If you're trying to define a variable or something, it would look like this:
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$trait = $mysidia->db->select("adoptable", array("Column"), "Row = '$somevalue'")->fetchColumn();
Then you can just use $trait to call it in the php file whenever you need it, instead of calling the table every time. (replacing trait with whatever you would call it of course)