A crowded board is easier to understand when you follow one vehicle's path and identify what must move before it.
Trace the whole path
Start with Traffic Tap Puzzle and check the movement rules. For each possible move, look beyond the next empty space: is the entire route clear? Where directions are fixed, use the displayed arrows rather than assuming a vehicle can turn. Find a vehicle that can leave without creating another obstruction.
Work backward from a blockage
If vehicle A is blocked by B, inspect B's route before repeatedly selecting A. Keep following that dependency until you find a legal move. After every departure, scan again because several routes may have opened. If movement is timed, also watch when paths cross; an empty destination alone does not guarantee a safe journey.