Because there are at most seven consecutive carbon atom, and four alkyl groups attached to the chain of carbon, I would name it 2,4-tetramethyl heptane.
Yes, it's tetramethyl heptane, where are the 4 methyls? 2,4,4,6-tetramethylheptane.
You are nearly right. You forgot to include that there is also a methyl group on carbon atom 6 and the name should also reflect that there are actually 2 methyl groups on carbon 4, so it's 2,4,4,6-tetramethylheptane.