Step 1: Recall the cofactor rule.
The cofactor of the entry in row $i$, column $j$ is $C_{ij}=(-1)^{i+j}M_{ij}$, where $M_{ij}$ is the $2\times2$ determinant left after deleting that row and column.
Step 2: Note the sign pattern for row 2.
For $i=2$ the signs are $(-1)^{3}=-,\ (-1)^{4}=+,\ (-1)^{5}=-$, i.e. minus, plus, minus across the three entries.
Step 3: Cofactor of the first entry $a_{21}=-4$.
Delete row 2 and column 1: $\begin{vmatrix}6&3\\-7&3\end{vmatrix}=18-(-21)=39$. With the minus sign, $C_{21}=-39$.
Step 4: Cofactor of the second entry $a_{22}=3$.
Delete row 2 and column 2: $\begin{vmatrix}5&3\\-4&3\end{vmatrix}=15-(-12)=27$. With the plus sign, $C_{22}=27$.
Step 5: Cofactor of the third entry $a_{23}=2$.
Delete row 2 and column 3: $\begin{vmatrix}5&6\\-4&-7\end{vmatrix}=-35-(-24)=-11$. With the minus sign, $C_{23}=-(-11)=11$.
Step 6: Collect the cofactors.
In order the cofactors of the second row are $-39,\ 27,\ 11$, matching option (2).
\[ \boxed{-39,\ 27,\ 11} \]