To all those who are embaressed by resorting to Fleming's left-hand rule :p there is an alternative way!
If you notice how we play around with our fingers to get the answer haha; we're actually positioning our fingers on axes..
Fleming's left hand rule says that the third finger is the current, second finger is the magnetic field and the thumb is the force.
Now, we can simply draw axes (including x,y,z) This can be seen in my attachment.
If the magentic field is on the x-axis (denoted as B), current is on the y-axis (denoted as I), then you begin to move from I to B, through the shortest distance between both. In this case, it is clockwise. Any clockwise rotation corresponds to a negative axis. And since the z-axis is the only one that has not been given, it must be on the negative z-axis. In other words, the force is into the page!
I hope I made this as simple as possible.
