The answer should be
" Her only regret was not dancing at the wedding "
Because a Gerund is an is a verb that functions as a noun. Wedding is a gerund because the word " Wed " is a verb e.g. " I am going to wed her " so when you add the " ing " it becomes a noun e.g. " I am going to a wedding "
That's why the last choice is the best one
Hope this helps!
