How do you clear the search engine history so when

when that list comes up, press the delete list to remove the entry.

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OK here you go bro.  This advice is from someone who actually uses a Mac.  Quit guessing.  Its me fool.
In Safari: select Safari at top tab, select preferences, select autofill, and uncheck all the boxes.
In Firefox: select Firefox at top tab, select preferences, select privacy, and uncheck all the boxes under history.  In the same box check Always clear private data when firefox closes.  Select clear now button and check all the boxes and select clear private data now. Now click Security Tab and uncheck remember passwords for sites so that they are not automatically filled in when you start typing in the first letter.
"Man is not complete until married, but is totally finished after marriage."