The technical definition of a number and its negative is that both numbers are the same distance away from zero, but in opposite directions on the number line, which is usually presented as a horizontal line with positive direction moving to the right. So the negative of 4 is -4 and the negative of -4 is 4.
This definition is simple but abstract, with no grounding in experience. Let's instead deal with something people understand where positive and negative movement make sense, our bank accounts.
A credit represents positive movement, money being added to our account, while a debit is negative movement, money being taken away. It is possible to have both negative credits and negative debits. If you put money in the account but the check you tried to cash bounced, the positive movement you thought you had has to be subtracted to reflect the true amount available. You can also have a negative credit, when money was removed from your account when it shouldn't have been. If there was a charge to your account that you didn't authorize or the bank charged your account some fee that you should have been exempt from, a negative debit means money going back into your account. This would be an example of a negative negative being a positive.
