Question

function:  mov eax,ebx   
           and ebx,1
           shl ebx,2
           jmp [ebx+Tab]
Tab:       dd F1
           dd F2
           dd F3
           dd F4
F4:        sub eax,eax
F3:        add eax,eax
F2:        sub eax,eax
F1:        ret

when ebx = Number–> should return Number in eax if is even otherwise 0

Answer 1

and ebx,1 Bitwise AND operation, results in either 0 (in case ebx is even) or 1 (otherwise)

shl ebx,2 Shift left by 2 bits (which is equivalent of multiply by 4). ebx is now 0 or 4.

jmp [ebx+Tab] Get adres from Tab + ebx and jump to it. Tab is array of four byte pointers, and ebx is either 0 or 4, so it points to first (F1) or second (F2) element.
In case of even number jump to F1 is taken (which returns original value), otherwise jump to F2 is taken (where eax is cleared and zero is returned).