Clue 6 has a lot of Xs for you. You basically determine what the left side cannot be, and reflect that as exclusions (Xs) for the two elements of the right side. Then turn it around and determine what the right side cannot be, and reflect that as exclusions (Xs) for the two elements of the left side.
If you do these types of clues later in the sequence, you will have a better chance of getting these extra Xs beyond the two obvious ones.
In this case, the left side of clue 6 doesn't have anything extra for us, but the right side has plenty.
The right side of clue 6 is either 120 or 3rd. We can see from the grid that 120 cannot be 1st or 2nd period. This means that the right side can only be 3rd, 4th, or 5th. So the left side can only be those periods.
Spanish cannot be 2nd, and Villareal cannot be 1st or 2nd period. This is going to determine that Algebra is 2nd period.
The right side of clue 6 also yields the fact that the only two rooms involved are 120 and 318. So the left side (Spanish and Villareal) can only be those two rooms as pointed out by Quazar.
The rest should fall into place pretty quickly.