Explanation:
: The structure of 2, 4, 4 trimethyl hexane are -

In -2 monohalogenated product by replacing two $\mathrm{CH}_3$ group at $\mathrm{C}_2$ and $\mathrm{C}_4$ Position and 4-monohalogenated product by replacing four $\mathrm{CH}_3$ group by $\mathrm{C}_2, \mathrm{C}_3, \mathrm{C}_5, \mathrm{C}_6$ Position.
Thus, the total no. of monohalogenated product formed by halogenation of 2, 4, 4 trimethylhexane are 6 .