The parallelogram rule say the tails (end without the arrow) of the two vectors at the same point, (just the a vector and b vector on the left of the diagram) then it asks you to close the parallelogram by drawing the same two vectors again (the b vector and a vector to the right of the diagram).

If we take, in the diagram, the two vectors above the green line we see that this is just the triangle rule for a+b and similarly the vectors below the green line are equal to b+a. The parallelogram rule is just the Triangle rule used twice at the same time, and really a demonstration that A+B=B+A

The head to tail rule asks that you take the tail of the second vector and place it at the head of the first vector. The head to tail rule applied to two vectors is simply the triangle rule.