Yamini asked Shifa if she would like to come for her birthday party the next day / the following day .
Alternative correct reporting:
Yamini asked Shifa whether she would like to come for her birthday party the following day.
Yamini invited Shifa to come for her birthday party the next day.
Yamini asked Shifa if she would like to attend her birthday party the following day.
Explanation of changes in reported speech:
\begin{tabular}{|l|l|}
\hline
Direct Speech & Reported Speech
\hline
Would you like & if she would like / whether she would like
\hline
my birthday & her birthday
\hline
tomorrow & the next day / the following day
\hline
\end{tabular}
Rules applied:
Question form changed to statement form
First person pronoun "my" changed to third person "her"
Time expression "tomorrow" changed to "the next day / the following day"
"Would" remains "would" (modal verbs often don't change)
"If/Whether" used to introduce the reported question