i think Lenz's law and induction is one of the most confusing topics in HSC physics..
Well lets say you move a single rod perpendicularly through a field. Since Lenz's law says its gonna make a magnetic field that tries to oppose the movement, then you put your palm in the opposite direction of movement. Your fingers point in the same way as the original field, and the thumb is hte consequent induced current direction.
You could also switch the direction of the field, but then you have to leave your palm towards the direction of movement, i.e. you can only change the direction of one of them.
Then theres the whole loop business. Imagine that loop in 10 iii) is outside of the field.. and then you move it into the field. This means there is relative increase in field lines, so Lenz's law says the loop has to make a field that decreases that field (that is.. opposing it) So you point your thumb down into the page, and your fingers are curled clockwise.
OR you take a test point in that same scenario. Use the length that enters the field first ( the furthest to the right). Since the thing is moving to the right, it needs to produce a resistive force to the left. So point your palm left, fingers up and thumb is downwards. follow that direction around the loop and you have clockwise.
This is what i've found after doing hours of this crap.... im not sure if it works in every situation... but so far it has. You just gotta get your hands on as many of these as you can, practice them and develop your own fail proof method, just so you don't lose simple marks in the exam.
