Indifference curves passing thru few points
The first sentence means that Tommy's mother's utility function over a bundle $(x,y)$ equals
\begin{equation*}
u(2,7)-u(x,y)=|x-2|+|y-7|
\end{equation*}
since she measures the disutility of this bundle with respect to the most preferred one by the "sum of the absolute values of the differences".

Therefore the utility that she associates with the point $(4,5)$ equals
\begin{equation*}
u(4,5)=u(2,7)-(2+2)=u(2,7)-4
\end{equation*}

You are asked to find the indifference curve that passes through the point $(4,5)$, i.e. the set of bundles $(x,y)$ that satisfy
\begin{equation*}
u(x,y)=u(4,5)
\end{equation*}
which you can write
\begin{equation*}
u(2,7)-u(x,y)=u(2,7)-u(4,5)=4
\end{equation*}

The question is therefore: which of the options a), b), c), d) (if any) contain only bundles $(x,y)$ such that $u(2,7)-u(x,y)=4$? You simply have to compute $u(2,7)-u(x,y)$ for all the proposed bundles, given the formula above, and check whether the value equals 4 or not.