- I learn English with watching movies.
Or, I learn English by watching movies.
- I clean my hands with soap and water.
Or, I clean my hands by soap and water.
I clean my hands WITH soap and water
In the first sentence, you use 'by' because 'watching movies' is the method of which you are learning English.
In the second sentence, you use 'with' because 'soap and water' are what you use to clean your hands.
You would say 'I play golf WITH a golf club', because the 'golf club' is what you are using to play golf.
You would say 'I'm teaching my students history BY showing them videos', because 'showing them videos' is the method of which you are teaching your students history.
Also, in your second sentence, it would be more common to say 'I wash my hands with soap and water'.
