The molecule 2,2-diisopropylheptane is incorrectly named. what is the correct name?

Isopropyl is: CH3 - CH - CH3
                                |

Heptane is: CH3 - CH2 - CH2 - CH2 - CH2 - CH2 - CH3

Then 2,2 isopropyl heptane is:

CH3 - CH - CH3
           |
CH3 - C - CH2 - CH2 - CH2 - CH2 - CH3
           |
CH3 - CH - CH3.

There you can count that the longest carbon chain has 8 carbon atoms.
So the right name is of an octane.

I will rearrange the chain to show the 8 carbon chain in a row:

           CH3   CH3
           |          |
CH3 - CH -   C - CH2 - CH2 - CH2 - CH2 - CH3
                      |
           CH3 - CH - CH3

Now, you can see that the right name is 3 isopropyl - 2, 3 dimethyl octane