The correct Active/Passive form of the given sentence is:

☀ No one ever taught me the rudiments of music.

Explanation for other options:

☀ No one have been ever teach me the rudiments of music. This option is not grammatically correct. The correct form should be "No one ever taught me the rudiments of music," not "No one have been ever teach me the rudiments of music."

☀ No one did ever teach me the rudiments of music. This option is not grammatically correct. The correct form should be "No one ever taught me the rudiments of music," not "No one did ever teach me the rudiments of music."

☀ No one ever taughted me the rudiments of music. This option is not grammatically correct. The correct form should be "No one ever taught me the rudiments of music," not "No one ever taughted me the rudiments of music." The past tense of "teach" is "taught," not "taughted."