How many teeth and sets of teeth does an elephant have?

They grow six sets of teeth in their lifetime which is no mean tusk.

The total number of teeth an elephant has is 24, six in each half jaw. No more than two of the six teeth are in wear at the same time in each side of a jaw (the only exception is in young elephants which may use three.) Teeth grow from the back of the jaw and follow a linear pathway of movement forwards as the preceding tooth is progressively worn down in the front. Each tooth drops out as it reaches the front of the elephant's jaw.

As an elephant gets older one of the most limiting factors in its ability to live a longer life is the teeth. Once the last molar the elephant has wears out it is incapable of chewing its food properly and either death from starvation or malnutrition will occur. Interestingly, about 10% of the older aged elephants will have an additional seventh molar, but it is never as developed as the others.

The tusks are actually upper incisors, not canines. They are the only incisors the elephant has. Tusks are fundamentally no different than ordinary teeth.

http://elephant.elehost.com/About_Elephants/Anatomy/Dentition/dentition.html

Elephants' teeth are very different from those of most other mammals. Over their lives they usually have 28 teeth. These are:

The two upper second incisors: these are the tusks.
The milk precursors of the tusks.
12 premolars, 3 in each side of each jaw.
12 molars, 3 in each side of each jaw.
https://en.wikipedia.org/wiki/Elephant#Teeth