Item 3.
First, reduce modulo 14:
\begin{equation*}
20x \equiv 23 \pmod{14}
\end{equation*}
\begin{equation*}
6x \equiv 9 \pmod{14}\text{.}
\end{equation*}
We could now divide both sides by 3, or try to increase 9 by a multiple of 14 to get a multiple of 6. If we divide by 3, we get,
\begin{equation*}
2x \equiv 3 \pmod{14}\text{.}
\end{equation*}
Now try adding multiples of 14 to 3, in hopes of getting a number we can divide by 2. This will not work! Every time we add 14 to the right side, the result will still be odd. We will never get an even number, so we will never be able to divide by 2. Thus there are no solutions to the congruence.