The absolute value [tex]|x|[/tex] returns the "positive version" of a number. In other words, if [tex]x[/tex] is already positive, then [tex]|x|=x[/tex]. Otherwise, if [tex]x[/tex] is negative, then the absolute value changes its sign, so that it returns positive: [tex]|x|=-x[/tex].
So, in this case, we have to plug the required values for [tex]x[/tex] in the expression [tex]2x-8[/tex]. Then, if the result is positive we're ok, otherwise we discard the negative sign.
We have:
[tex]x=-2.5 \implies |2x-8| = |-5-8|=|-13|=13[/tex]
[tex]x=0 \implies |2x-8| = |0-8|=|-8|=8[/tex]
[tex]x=4 \implies |2x-8| = |8-8|=|0|=0[/tex]
[tex]x=5 \implies |2x-8| = |10-8|=|2|=2[/tex]
[tex]x=9.5 \implies |2x-8| = |19-8|=|11|=11[/tex]
