To name an organic compound by the IUPAC system, you (1) identify the principal functional group, (2) select the longest continuous carbon chain that contains that group as the parent, (3) number the chain from the end that gives the functional group the lowest locant, and (4) add substituents with their position numbers. Here the compound is CH₃–CH₂–CH(CH₃)–CH₂–CH₂–OH.

Step-by-step:

• The functional group is the hydroxyl (–OH) group, so this is an alcohol (suffix -ol).
• The longest chain that includes the carbon bearing –OH has five carbons → parent is pentane.
• Numbering must give –OH the lowest number. Counting from the end nearest the –OH: C1 carries the –OH, C2 is CH₂, C3 is the CH that carries a –CH₃ branch, C4 is CH₂, C5 is CH₃. So the –OH is at position 1 and the methyl branch is at position 3.
• Assembling the name: 3-methylpentan-1-ol.

Now the incorrect options:

• 3-methylhexanol and 2-methylhexanol use "hex" (six carbons), but the parent chain here has only five carbons, so a hexane root is wrong.
• 4-methylpentanol has the right five-carbon root but the wrong numbering — if you counted from the far end you would place –OH at C5 and the methyl at C3, and IUPAC rules require the –OH (the principal group) to get the lowest locant, i.e. C1, which forces the methyl to position 3, not 4.

Hence the systematically correct name is 3-methylpentan-1-ol.