The first three examples above are correct. The first example has the active verb “mailed” used with the object “package”; the second example has the passive verb “was mailed” used with “by us”; the third sentence has the passive verb was mailed used without an object.

The fourth example is the type of passive error that appears most often on the TOEFL test. This type of sentence has the following characteristics:
1. an incorrect passive verb that looks like a correct active verb, and
2. no by + object to tell you that a passive is needed.

To correct the fourth example, the active verb needs to be changed to the passive “was mailed”.

To determine that such a sentence is incorrect, you must study the meaning of the subject and the verb. You must ask yourself if the subject” does” the action of the verb (so an active verb is needed) or if the subject “receives” the action of the verb (so a passive verb is needed). In the incorrect example, you should study the meaning of the subject and verb, “the letter mailed”. You should ask yourself if “a letter mails itself” (the letter does the action) or if someone mails a letter (the letter receives the action of being mailed). Since a letter does not mail itself, the passive is required in this sentence.