Rewrite the sentences using inversion. Startwith the words in brackets .
She had only just woken up when the builders arrived.(hardly)
the solution is :Hardly had she woken up when the builders arrived.

Why is had she and not she had?
I wrote the sentence like this :
Hardly she had woken up when the builders arrived. Is it bad?

Question

Rewrite the sentences using inversion. Startwith the words in brackets .
She had only just woken up when the builders arrived.(hardly)
the solution is :Hardly had she woken up when the builders arrived.

Why is had she and not  she had? 
I wrote the sentence like this :
Hardly she had woken up when the builders arrived.   Is it bad?

Answer

"Hardly she had" just sounds strange.  It is because we tend to keep the adverb (hardly) next to the verb (had) that it modifies.  Some things also sound clumsy in a language, just because of the way the language has developed.