First of all notice m^2 is always non-negative, so -m^2 is non-positive (zero or negative), which means that y is zero when m=0 and y is negative for ANY other value of m.
I. y is negative --> not necessarily true, if m=0 then y=-m^2=0;
II. m is non-negative. m can take ANY value: positive, negative, zero. We don't have any restrictions on its value;
III. If m is negative then y is negative. m is negative means that m is not zero. As discussed above if m is other than zero (positive or negative) then y is negative: y=-(negative^2)=-positive=negative (y=-(positive^2)=-positive=negative). So, this option is always true.
Answer: C (III only).