The Beery assesses the ability to co-ordinate fine hand and eye movements (Visual Motor Integration-VMI).
It would be part of a battery of standardised tests that OTs use in assessing a child with possible dyspraxia.
It doesnt look at visual processing in depth; a separate test for Visual Perception would usually be also used.
So if the child had good Visual Perception but poor VMI, then we could assume that they have poor ability to co-ordinate eyes and hands; so therapy would focus on that.
If they had poor Visual Perception, then it would be usual to also have a poor VMI as the hands are co-ordinating with inadequate visual info IYSWIM. Therapy would then, initially, work on Visual Perception, then tying it to hand function.
For instance, if you are driving with a dirty windscreen which makes it difficult to see through; which is the problem, your ability to drive, or your ability to adequately see? If you clean the windscreen (Visual Perception) and your driving doesnt improve then we can safely assume, it's your driving that needs work. (Very rough analogy but I hope it explains).
It would be usual to also do a test of gross and fine motor skills to see if the difficulty is movement in general, or confined to when the child has to co-ordinate hands and eyes.
Hope that helps. Please ask if I havent explained it well.
Not understanding something on a book or whiteboard could be dyslexia (which has a 50% co-morbidity with dyspraxia) or it could be Visual Perception.
It could also be difficulty with cogntive processing which is a feature of dyspraxia.
The VMI is giving you one aspect of the problem and not enough information alone to answer your questions.