justify the position of carbon in group 4 and second period ?​

In modern IUPAC notation, it is called Group 14. In the field of semiconductor physics, it is still universally called Group IV. The group was once also known as the tetrels (from the Greek word tetra, which means four), stemming from the Roman numeral IV in the group names, or (not coincidentally) from the fact that these elements have four valence electrons

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Carbon has electronic configuration as

[tex]1s {}^{2} 2s {}^{2} 2px {}^{1} 2py {}^{1} [/tex]

So it has the 4 electron in the outermost shell so it lies in 4 group

Also it have only 2 shell so it belongs to the 2 period