Do damage or make damage?
Which verb is correct?
In both British and American English you can do, cause, incur or suffer damage. You cannot "make" damage.
Study the following example sentences:
Unsupervised TV watching would do damge to the child.
Obama's plans could do damage to entrepreneurs and small business owners.
The radiation causes fatigue and can do damage to the lungs and heart.
The Internet has the power to do damage through misinformation or sabotage.
However, it is sometimes possible to put the verb "make" before the noun "damage", but it is only a coincidence and the meaning is never "to do harm or cause injury".
For example: What should I do to make damage less visible?
Remember that "damage" is an uncountable noun, so you can never say "do a damage"
or "do damages"!