Which of the following is the correct iupac name?
(a) 4−ethyl−6,6−dimethylheptane
(b) 2,2−dimethyl−4−propylhexane
(c) 4−ethyl−2,2−dimethylheptane
(d) 3−propyl−5,5−dimethylhexane

(C) 4-ethyl-2,2-dimethylheptane.

Explanation:

Step one: draw the carbon skeletons of each "IUPAC name" as if they were accurate. Note that

Hexane: a carbon backbone of six carbon atoms, linked in a row with carbon-carbon single bonds.Heptane: a carbon backbone of seven carbon atoms, linked in a row with carbon-carbon single bonds.A methyl group is a one-carbon substitute -CH₃ for an H atom on the backbone.An ethyl group is a two-carbon substitute  -CH₂-CH₃ for an H atom on the backbone.A propyl group is a three-carbon substitute -CH₂-CH₂-CH₃ for an H atom on the backbone.

Step two: check the structures and the names against the IUPAC rules.

There are many of these rules. Ones that apply here include:

The backbone shall be named after the longest chain of carbon atoms. There may be right angles but the chain needs to be continuous.List the substitutes in alphabetical order (e.g,, ethyl, methyl, and propyl.)Number the substitutes from the end that ensures the smallest number for the first substitute group that is encounter. If starting from both ends lead to the same number for the first group, check the second group.

Refer to the sketch attached.

(A)

Should start numbering from the other end.

(B) and (D)

The longest backbone contains seven carbon atoms.