FOR ALL POSITIVE INTEGERS m, m(there is a box around m)= 3m(no box here m) when m is odd and m(there is a box around m)=1/2m(no box around m here) when m is even. Which of the following is equivalent to 9 times 6(there is a box around each 9 and 6).

The answer is 27.

What's the best way to solve this problem

Please disregard. Thanks...

actually. i need an explanation for this.

the way you've transcribed the problem, the answer should be 81, not 27, unless the answer 27 is also in a box (which is probably the case - i bet you just forgot to mention this)
if there's a box around a 9, then, according to the rule promulgated above, that means 3 x 9, or 27.
if there's a box around a 6, then, according to that same rule, that means (1/2)(6), or 3.
27 x 3 = 81.

if the 27 you've cited as the answer is also in a box, then, since 27 is odd, that's actually 3 x 27, or 81.
if the 27 is not in a box, then it's the wrong answer.