name this compound using IUPAC system?

Brit: 2-methylbuta-1,3-diene
U.S. 2-methyl-1,3-butadiene

The parent chain contains 4 carbon atoms and 2 C=C double bonds, with one between C₁ and C₂, and another between C₃ and C₄. So, the parent chain is named as buta-1,3-diene (Brit.) or 1,3-butadiene (U.S.).

There is one methyl group (-CH₃) at C₂ (counting for the leftmost and getting the smallest number). Therefore, the IUPAC name of the compound is 2-methylbuta-1,3-diene (Brit.) or 2-methyl-1,3-butadiene (U.S.).

However, as there is no ambiguity for the position of the methyl group (i.e. it must be at C₂, while other positions are impossible), the numbering of the methyl group can be omitted. Therefore, the IUPAC of the compound can also be methylbuta-1,3-diene (Brit.) or methyl-1,3-butadiene (U.S.).

3-methyl-1,3-butadiene
the longest continuous chain is 4 carbons, which would be butane. It has 2 double bonds, making it butadiene, a 1,3 butadiene at that. A methyl group is attached to the 3rd carbon, making it 3 methyl derivative. This is just a guess, but I think it may be correct.