Heres the sentence :
彼は自由なほうの手を伸ばして頭皮をさわり、痛みの源を突き止めようとした。
So I understand the sentence, I think, by context, as : "He reached up with his free arm and touched his scalp, trying to determine the origin of his headache."
But i can't find a good definition or explanation for this "ほう", which kanji is this related ? what's the meaning here ?
Thanks in advance.
The kanji that's it's representing is the standard 方. It is used in the standard way of making a comparison between two objects. Here the comparison is between the two hands of the person. As for what comparison it's making, the answer is that it's comparing the 自由-ness of the two hands. So here 自由なほうの手 means the hand that is more 自由.
Edit: As Chocolate points out, 方 when used here isn't actually making a comparison between the level of 自由, but the existence of 自由 or not.
making a comparison between two objects. it's comparing the 自由-ness 自由なほうの手 means the hand that is more 自由. -- それは「二者を取り上げて比較した時の一方。 『兄より弟の方が背が高い』」（大辞林）の用法ですよね。ここでの「自由な方の手を伸ばして…」の「方」は、「対立的に存在するものの一方。がわ。 」(大辞林) の用法ですよね。「2本ある手を比較して、比較的、より自由な方の手 (the more free hand between the two hands)」って意味じゃなくて、「自由な手と自由でない手があって、その自由な方の手(the free hand, not the other not-free hand)」(「自由なほうの手」というからには、「自由でない手」が存在する)ですよね。