just plug in values. like when t =0, equation A is at (1,0,0), so we can rule out a lot of cases. similarly we know that equation A will increase linearly rather than sinusoidslly in j coordinate, whereas in i and k coordinate the values will oscillate. so we know equation A matches the bottom middle picture (although their diagram is terrible)
pretty much just repeat that process, plug in more values like pi, pi/3, 2pi, etc if u get stuck