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I was practicing and I'm having trouble diagramming/understanding this game. There are a few games that I have come across that has a similar set up, but I have trouble with those as well.

PT 34
section 4
game 4

6 doctors J,K,L,N,O,and P are at one of two clinics, S and P.

K is at R if J is at S
O is at S if J is at R
If L is at S then N and P are at R
If n is at R then so is O
If P is at R then both K and O are at S

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On rule number 2 if J is not at R, then that means O is automatically at R right?
On rule number 5 how can K and O be at S if rule 1 puts K at R and rule 2 puts O at R as well?

Rule 1 and Rule 4 contradict each other especially on number 19. How can J,N,O,P be the correct answer if J and K can't be together rule 1. How does rule 1 get disregarded when applying rule 4?

The easiest way to approach this game is to chain together the rules and their contrapositives:
LS --> NR --> OR --> JS --> KR --> PS --> LR
Since starting from LS leads to a contradiction (LR), we know that L cannot be assigned to S. Creating the contrapositive of the chain gives:
PR --> KS --> JR --> OS --> NS --> LR

washin34 wrote: On rule number 2 if J is not at R, then that means O is automatically at R right?

You're making a mistaken negation (negating both sides). To correctly create the contrapositive, you must negate both sides and reverse the order: OR --> JS

washin34 wrote:On rule number 5 how can K and O be at S if rule 1 puts K at R and rule 2 puts O at R as well?

Remember that these are conditional statements. The rules don't tell us definitively who is assigned where; rather, they tell us who is assigned to which clinic when certain conditions are met.

washin34 wrote:Rule 1 and Rule 4 contradict each other especially on number 19. How can J,N,O,P be the correct answer if J and K can't be together rule 1. How does rule 1 get disregarded when applying rule 4?

You're incorrectly interpreting rule 1. Taking its contrapositive gives KS --> JR. Thus, rule 1 allows for three possible outcomes:
JS, KR
KS, JR
JR, KR