Arrange in order terror, terrace, terminate, terminal
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terminal, terminate, terrace, terror.

Explanation:

The above is an alphabetical arrangement of words starting with the letter, T.

All the words have the same first three letters. Since letter m comes before letter r, 'terminal' and 'terminate' will come before terrace and terror.The words, 'terminal' and 'terminate' have the same first seven letters. Since letter l comes before letter t, the word 'terminal' will thus come before 'terminate'. The words, 'terrace', and 'terror' have the same first four letters. Since letter a comes before letter o, 'terrace' will come before 'terror'.