In this ray diagram, a plane mirror seems to form a real image In this ray diagram the image formed seems to be real with the given position of the  eye. I have learnt that plane mirrors cannot form real images at any circumstance. But at this one it does. Please explain the answer like I'm 5 and how you deduced what you propose.

 A: Some diverging rays have been left out as shown below!

A cone of diverging rays which appear to come from $B_1$ are reflected off the mirror and the eye focuses those rays onto the retina to form a real image of the bottom of the feet.
A: Farcher's answer is correct. But it can be elaborated a bit to make it easier to understand.

If you observe the above ray diagram for real images, you can see that the real images are formed when rays from the same point of an object intersect to form an image.
As your image shows, this is not the case. Rays from the top and bottom of the object intersect at the eye. Hence the image formed is not real.
As Farcher's modified image shows, the rays from the same point never intersect, but diverges. Hence the image formed is virtual.
A: When one says that a plane mirror cannot form an image, what they mean is that if a collection of parallel light rays are incident on a mirror, the reflected rays will not converge to a point.
Of course, if the rays are already converging to a point when they reflect off the mirror, then they will continue to do so afterward.  That is what seems to be shown in your figure.
