You know that if 2 lines are parallel, they have the same slope.
First, find the slope of the given line;
y+10 = 23(x-8)
y=23x-184-10
y=23x-194
Slope is 23
Write out the basic format;
y=mx+c
y=23x+c <--- replace x and y values here
-5=23(6)+c
-5-138=c
-143=c
Therefore, this equation would be y=23x-143
Hope I helped :)