This LSAT ordering game requires that you see the interrelationships among the elements.
Diagram
Use an ordering diagram, but recognize that you will use the diagram little on a game such as this one. Instead, you will focus on the interrelationships that exist given in the conditions.
Conditions
The four conditions show the interrelations among the elements which should all be combined to produce one complex condition:
Note that position from left to right means nothing. For example, H is situated to the left of J, but no lines interconnect H and J, thus, it's possible that H is before J, or that J is before H.
instead, focus on the lines and what those lines tell you about relationships between and among elements.