You have shown no structure, still we can work out for the answer :).
First Option: 2-dimethylyne: This name is incorrect, because it does not contain any parent chain name.
Second Option: 2-methylbutane: I have drawn its structure below, compare it with your structure.
Third Option: 4-methylbutene: I have drawn the structure for this name. But this name is also against IUPAC rules, and its correct name is 1-Pentene.
Fourth Option: 4,3-methylbutyne: Again incorrect name, 4,3 are two positions, but here only one substituent is given (methyl). I have drawn structure of 3,4-Dimethylbutene, this name is incorrect, and the correct name for this compound is 3-Methyl-1-pentene.
Fifth Option: 4,4-methylbutane: Again incorrect name, 4,4 means at 4 position two substituents, but in name only methyl is given. Anyhow lets make it two and draw a structure, for 4,4-Dimethylbutane. Ooops!! This name is also incorrect, and the correct name for this compound is 2-Methylpentane.
Result:
Among all options only, option B (2-Methylbutane) is correctly named, and this will be the correct name for the structure given to you.
