Level 604 seems to have no pattern in the how or when things fall.
Pets, blocks, metal blocks, balloons and even bombs all fall randomly.
x2 blocks seem to mainly fall in the central column and the two outer columns.
Line blasters only fall in the center and two outer columns too.
Concentrating on one side, or the center can help as you’ll have more line blasters drop.
The main problem though, is that because the pets are random too, you can go half the game without even seeing one!
Charge up the rockets as best you can, use them to destroy one side of the mesh machines (make a match beside them first to clear any mesh), this will give you a good space of board to work on.
Make big matches to charge up rockets.
Some of the pet carriers are in a different color to the blocks, use the rockets on them.
If there are more than one pet in a column, use a rocket on them.
If you’re planning on rocketing them, don’t waste a move getting the pet out of it’s carrier.
Also, use the rockets as much as possible on the central column, or an outer column, to get line blasters dropping so you can also make good use of them!