Answer
The formula of the compound is:
$3-ethyl-2,6,7-trimethyloctane$
Work Step by Step
The longest carbon chain has 8 carbon atoms (-oct). There are 3 methyl substituents, one each on positions 2, 6 and 7. There is an ethyl substituent on position 3. Listing the substituents in alphabetical order, the formula of the compound is:
$3-ethyl-2,6,7-trimethyloctane$