Why can't $|x-2|$ be less than zero? Just confused with the concepts in Absolute Value.
So we know that to solve absolute value equations such,
$$|x-2| = 5 \tag1$$
In this case we have, $x-2 = 5$ and $x-2 = -5$. then solve for $x$.
However,
$$|x-2| = -5 \tag2$$
Here is no solution.

Why can't the absolute value be less than zero?

Is it from a graph that we cannot get negative values from the $y$-axis? Are there any other explanations?
A proof is highly appreciated.

What's called absolute value of  a number is just the numbers's distance from zero.  As such it's always non-negative. Furthermore $|a-b|$ is the distance from $a$ to $b$.
Your first equation, $|x-2|=5$ reads: "The distance from $x$ to $2$ equals $5$.", hence $x=-3$ or $x=7$.  Now the second equation, $|x-2|=-5$, reads: "The distance from $x$ to $2$ equals $-5$.", which is impossible.
