`->` She said that she would come back the following day.

`----------`

$\rm -$ cấu trúc câu tường thuật ( reported speech )

$\rm S+said(that)+S+V_{(lùi\ thì)}+O$

`--------`

the following day `->` tomorrow (simple future )

will come $\rm \xrightarrow{lùi\ thì}$ would come

(simple future `->` future in past )