Is it permissible to mention the teacher's flaws if he does not explain well and puts the wrong solution in the teacher's book?

Backbiting is to mention about your brother that which he dislikes. If what you mentioned about your teacher is something he dislikes, then this is backbiting. The criterion is to mention about a person something that is true about them but which they dislike, whether it pertains to their body, religion, worldly affairs, appearance, character, wealth, children, spouse, servant, slave, clothing, gait, movement, cheerfulness, looseness, frown, or openness. This applies whether you mention it verbally, in writing, or by hinting or pointing with your eye, hand, or head. If the teacher is unfit for teaching, the officials in the school administration should be informed without exaggeration or understatement; in this case, it is permissible to mention this fault.