I'm a little confused as to why the P0: LD Y operation would cause cache 1 to put X into the I state. Because nothing happened to X right, so the variable should still be correct and shared among both cache 0 and cache 1 right? So why does loading line Y cause line X to be put into the I state for cache 1?

@derrick. Good catch. That should say "do nothing, line Y is in the I state".

However, notice that if you go two rows up, P0 wrote 4 to X. Therefore, P1 would have X in the I state starting at that point. So even if the line you are talking about is a LD of X (and not Y), P1 would still do nothing as it would already have line X in the I state.