At first glance my immediate answer was "in", but I've heard both used and would consider both acceptable. When I google "in his intentions" and "about his intentions", I get about twice as many hits for "in his intentions".

The answer is B (about)

I see now, "He's quite honest in his intentions" says something about the intentions themselves, and "He's quite honest about his intentions" says whether he was honest with people (about his intentions). Thanks Saj!

They're both correct, but mean different things. "He's quite honest in his intentions." means that his intentions were good, and that he didn't intend to be deceitful or to lie. "He's quite honest about his intentions." means that he's honest and upfront about his motivation for something, no matter what the motives may be.