can macbook air install "macOS High Sierra" 10.13.6?

A mid 2011 can install High Sierra.

See instructions in see instructions in: How to download and install macOS - Apple Support

Be sure to have a current backup before upgrading (a good idea even when not upgrading).

Also see the following from Identify your MacBook Air model - Apple Support

MacBook Air (13-inch, Mid 2011)

Model Identifier: MacBookAir4,2

Part Numbers: MC965xx/A, MC966xx/A

Newest compatible operating system: macOS High Sierra