You may choose to calculate moments about any point that you want. You have a total of 6 equations to play with at any point (three for forces in x, y, and zdimensions and three for moments about x, y and zaxes). So as long as there are no more than 6 unknowns you should be able to find a solution (if one exists) no matter which point you choose to use as O, and no matter which particular directions you choose for x, y and zaxes (as long as they are independent, or better yet orthogonal to each other). However, by using some judgment about selecting which point to use and which way the axes are oriented you can often reduce these 6 equations to a more manageable number, thus making the problem much easier to solve. For example in this problem by selecting axes x', y' and z' the 6 equations simplify to become just two.
