For the specific state \( E_1 \), we have chosen all spins up. The energy of this configuration becomes then $$ \begin{equation*} E_1=E_{\uparrow\uparrow}=-J. \end{equation*} $$ The other configurations give $$ \begin{equation*} E_2=E_{\uparrow\downarrow}=+J, \end{equation*} $$ $$ \begin{equation*} E_3=E_{\downarrow\uparrow}=+J, \end{equation*} $$ and $$ \begin{equation*} E_4=E_{\downarrow\downarrow}=-J. \end{equation*} $$