Contract is 4 H.
Opening Lead: K S.
Start by counting losers. 2 Spade losers; 0 Heart losers; 1 Diamond loser; and possibly 1 or more Club losers. The only chance to make this contract is to keep the Club losers to 0. That means ruffing 4 Clubs in Dummy. Therefore, not even one round of trump can be played. 
Problem: how to get back to the hand to lead Clubs. The only way is to ruff Diamonds, that is, crossruff the two minor suits. But in order to crossruff you have to give up the lead in Diamonds to clear that suit from Declarer's hand. A good defender after winning the trick in Diamonds and cashing the 2 Spade winners, will lead a trump. You will now only be able to ruff 3 losing Clubs in  Dummy. 
Solution: win the trump return in Dummy and take the Club finesse. If it wins you will make the hand by crossruffing. Play the A C; ruff the 1st Club; ruff a Diamond; ruff the 2nd Club; ruff a Diamond; ruff the 3rd and last Club. You are left with only one high trump in your hand. Bid and made 4 H.

Contract is 6 H.
Opening Lead: K C.
This time count winners. 1 Spade winner (the Ace) and 3 ruffs in the hand; and 1 Club winner (the Ace) and 4 Club ruffs for a total of 9 tricks. The other 3 winners needed to make the Slam are coming from the 5th trump and the Ace and King of Diamonds. 
Problem: if the crossruff in the black suit is complete, there will not be enough trump left to extract defenders trump. Then two Diamond winners might  be ruffed. 
Solution: there is a slight risk, but the Crossruff Rule must be follwed. Cash the Ace and King of Diamonds before ruffing. Win the opening lead with the A C; play the A D, then K D; A S and ruff the 1st Spade. Ruff a Club; ruff the 2nd Spade; ruff a Club; ruff the 3rd and last Spade. Your hand now  has two high trump and a losing Diamond. Bid and made 6 H.

S  9 8 3 
H  K Q 8 7 
D  K 9 7 6 4 
C  3 


S  A 10 2 
H  A J 10 9 
D  5 
C  A Q 7 4 2

S  9 
H  A J 5 2 
D  A 9 4 
C  A 8 6 5 4 


S  A 8 6 4 
H  K Q 10 9 7 
D  K 6 3 
C  2

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