In the group $\{1,2,3,4,5,6\}$ under multiplication $\bmod 7,2^{-1} X_{7}^{4}=$

Under Multiplication Modulo 7 , inverse of 2 is $2 \times 4=1(\bmod 7)$ Hence, $\quad 2^{-1}=4$ Now, $2^{-1} \times 4=4 \times 4=16$ Now, $\quad 16=2 \times 7+2$ Hence dividing 16 by 7 gives a remainder 2 , Therefore, value of above multiplication mod is 2.