1.  Partner leads the 2.
List  6 thngs we know about p's and declarer's hand.
1) He has 4 spades (he led the 4th down and there are no lower ones in his hand since you can see them)
2) He has no 5 card or longer suit
3) His distribution is either 4441, 4432, 4333
4) Spades are his strongest 4 card suit
5) He doesn't have a sequence in any suit
6) We know how many spades declarer has
2.  Partner leads the 6.
The 6 is the lowest outstanding spade. Assuming it is fourth highest, West has only a fourcard
spade suit.
Declarer must only have 3.  (4 to partner, 3 in dummy, 3 in my hand… that leaves only 3 for declarer)
3.  Partner leads the 7.  How many spades does partner have?
4 or 5:
The 7 might be his 4th card from a 4 card suit - but it might be his 4th down from a 5 card suit.   
We can't see the 6 so Partner might have it which give partner 5 cards in the suit.  We can't tell
until we see the 6.  (The 6 is the only lower card missing below the 7.)
If declarer
plays the 6 at some point during the play, East will know that West started
with only a four-card suit. If West plays the 6 at some later point in the
play, East will know that West started with a five-card suit — assuming East
remembers that West originally led the 7.
4.  Partner leads the 7, dummy plays the 3.
East should play the 2, letting West’s 7
win the trick! If the 7 is West’s fourth highest card in the suit, West must
also hold the Q, 10 and 8, since these are the only three spades
higher than the 7.
5.  If east doesn't  play the 2..
If east were to play the 9 or the J on the first trick, East would win the trick and be on lead. East couldn’t
lead the suit a second time, without giving a trick to dummy’s K.
6.   What does the lead of the 4 tell partner?
Partner has 4 spades. (You can see the 2 and the 3).
The rule of eleven means declarer has 2 cards in the suit and both are higher than the 4 (there
are no lower ones left!)
Eleven minus four is seven. East can see two higher
cards than the 4 in dummy, the K and the 5. East holds three higher
cards, the A, the J and the 9. That leaves two cards higher than the
4 in declarer’s hand
      What card should East play if dummy plays low?
East knows declarer has 2 cards in the suit - Partner has 4, dummy 3 and east holds 4.
The only card higher than Dummy's King and East's ace is the Queen.  East won't know if 
declarer has the queen or not, so east plays the highest card he can play while still keeping the honor
over the King - East plays the Jack.
We've learned that if declarer has the king and the queen in a suit, he is entitled to one trick.
If east plays the ace when dummy plays low, declarer will get two tricks, the king AND the queen!