Write an absolute value equation that has the solutions x=−6 and x=10

Remember, if |a|=b then assume a=b and a=-b

let's start with x=-6 and x=10

find their average
-6+10=4
4/2=2
average is 2
now subtract that from the lower and minus it from the larger
-6-2=-8
10-2=8
|8|=|-8|=8

so we know that it will be
|x-2|=8
if we solve

x-2=8 or x-2=-8
add 2
x=10 or x=-6

a possible equaton is |x-2|=8