How are there three possible tautomers of 2,2,4-trimethylheptane-3,5-dione?
In your attempt the 4th compound is not reported to have significant percentage in solution (acidic or basic). This is because once the tautomerisation occurs for example let's say the 1st compound, there is a tautomer having a six-membered conjugated ring involving H-bonding. This thereby increases the stability of the compound and consequently increasing the activation energy for the tautomerisation you proposed in compound 4. This is why compound 4 is not formed.

Also keep in mind that stereo-chemistry is also important while finding number of possible compounds.