Correct Option: D

As we know that
4¹ = 4;
4² = 16;
4³ = 64;
4⁴ = 256;
4⁵ = 1024;
As we see that
Unit place of 4¹ = 4;
Unit place of 4² = 16;
Unit place of 4³ = 64;
Unit place of 4⁴ = 256;
Unit place of 4⁵ = 1024;
Unit digit is repeating after every 4th index number.
Remainder on dividing 372 by 4 = 0
Remainder on dividing 373 by 4 = 1
∴  Required unit digit = Unit digit of (124)³⁷² + (124)³⁷³
∴  Required unit digit = Unit digit of (4)³⁷² + (4)³⁷³
as we know that Remainder on dividing 372 by 4 = 0 and Remainder on dividing 373 by 4 = 1
∴  Required unit digit = Unit digit of (4)⁴ + (4)¹
∴  Required unit digit = Unit digit of of sum of ( 6 + 4 )
∴  Required unit digit = Unit digit of of sum of ( 10 )
∴  Required unit digit = 0