$\color{green}{a^*(ab+ba)^*b^*} = \color{blue}{\{\epsilon, a,} \color{red}{b}, \color{blue}{aa, bb, aaa, bbb,abba,........\}}$
$\color{green}{a^*b^*b(a+(ab)^*)^*b^* }= \color{blue}{\{}\color{red}{b},\color{blue}{ aa, bb, ab,aaa, bbb, aba, bba, aab, abba,........\}}$
So, Both the expressions are having $\color{red}{b}$ as a shortest common string.
So option d is correct.