$2^{1}=2 \ ; \ 2^{2} = 4 \ ; \ 2^{3}=8 \ ;\ 2^{4}=16$
$2^{5}=32 \ ; \ 2^{6} = 64 \ ; \ 2^{7}=128 \ ;\ 2^{8}=256$
From above it is clear that the Cyclicity of 2 is 4.
$2^{51}=2^{48}\times 2^{3}$
Unit place of 48=6
Unit place of 49=2
Unit place of 50=4
Hence, unit place of $2^{51}=8$
Hence,Option(B)8.