could anyone help me to get the difference between numb, dope, anesthetize and drug when we use them as verbs?
explanation with example would be appreciated.
The words are all sort of related, though some are more slang-y and others are technical. I'm going to assume you mean the definitions that relate to each other and not the broader meanings. So, here they are, in order from most technical to least (in my opinion).
This is the technical term for the act of numbing a patient before a medical procedure:
medical : to give drugs to (a patient) so that no pain can be felt : to give an anesthetic to (a patient)
The doctor anesthetized the patient [with] an intravenous injection.
As a verb, this means the same thing as anesthetize but it's a non-technical term, often used when talking directly to patients who may not know what the technical term means or by patients who don't want to use the technical term:
To cause to become numb.
The dentist gave me Novocaine to numb my tooth before drilling, thank goodness.
"I'm going to numb the area before we get started with the procedure."
It can also be more generally used, outside of the medical world:
to make a part of your body unable to feel anything, for example because of cold
His fingers were numbed with the cold.
This is used much more broadly than anesthetize because, while anesthetics are a type of drug, there are many others. This generally carries a negative connotation, though, so use with caution:
to give a person or an animal a drug, especially to make them unconscious, or to affect their performance in a race or competition
He was drugged and bundled into the back of the car.
He was asleep, heavily drugged with tranquillizers.
It could also be used more informally/colloquially:
The doctor drugged me before the operation and I didn't feel a thing.
Dope is much more slang, though it's being used more and more in relation to sports drug use. The verb definition is almost identical to drug.
to give a drug to a person or an animal in order to affect their performance in a race or sport
The wine was doped.
It can be used, very informally, in the medical sense:
I was so doped up on morphine, I don't remember anything that happened.