Considering that # |\frac{a}{b}|= \frac{|a|}{|b|}#, you get that #|\frac{m}{8}|=1# if and only if #\frac{|m|}{|8|}=1#.
Now, obviously #|8|=8#, since 8 is a positive number and the absolute value of a number is the number itself is the number is positive, and the opposite otherwise.
So, we can rewrite the equality as #\frac{|m|}{8}=1#, which yields #|m|=8#
This request has two solutions. In fact, if #m# is positive, then #|m|=m#, and so we have #m=8#.
Otherwise, if #m# is negative, we have that #|m|=-m#, and thus #m=-8# solves the equation.
We conclude that #|\frac{m}{8}|=1# if and only if #m=\pm 8#
