How two phases locking ensures serializable?

I have read many sources , and they say one of the ways to implement serializable in the database is to use two-phase locking. But I don't really understand how two-phase locking could ensure serializable in this example from Jim Gray. An example is we have two rows in the database, one has the value of **white** and the other one has the value of **black**. I have two transactions: - TX1 will update the value of **white** to **black** - TX2 will update the value of **black** to **white** If TX1 and TX2 are executed at the same time, then TX1 acquires the lock on the row with the value of **white**, and TX2 acquires the lock on the row with the value of **black**. So there are no locking conflicts, and eventually, the values are swapped.