Well I’m not much for drawing diagrams in chat rooms, but I can attempt to explain Elizabeth’s heirs.
First Generation:
Queen Elizabeth
Second Generation (Elizabeth’s children):
Prince Charles
Princess Anne*
Prince Andrew
Prince Edward
*Note that as a girl, Anne is lower in the order of succession than her younger brothers.
Third Generation (Elizabeth’s grandchildren):
(Charles’s children)
Prince William
Prince Harry
(Anne’s children)
Peter (not a prince, but does qualify)
Zara (not a princess, but does qualify)
(Andrew’s children)
Princess Beatrice
Princess Eugenie
(Note that Beatrice and Eugenie are higher in the line of succession than Peter and Zara because Andrew is male.)
(Edward’s children)
Louise (not a princess, but does qualify)
James (not a prince, but does qualify)
Fourth Generation (Elizabeth’s great-grandchildren):
(Charles’s grandchildren, William’s children)
Prince George
Princess Charlotte*
Prince Louis
(Charles’s grandchild, Harry’s child)
Archie (not a prince, won’t qualify until his grandfather, Charles, is monarch)
(Anne’s grandchildren)
4 total, 2 from each of her kids, none princes or princesses and don’t qualify
(Andrew’s grandchild)
1 grandson from Eugenie (not a prince, doesn’t qualify)
Edward does not yet have any grandchildren. They will not be princes or princesses when they come.
*They changed the rules of succession to get rid of male preference for children born in or after… whatever year George was born. Thus Charlotte did not lose her place in line to her little brother though it is unlikely to be relevant.