The first side of a triangle is 8m shorter than the second side. the third side is 4 times as long as the first side. the perimeter is 26 m. find the length of each side

Call the length of the second side ' S ' .
(It could have any name.  I just felt like calling it ' S ' for 'second'.)

The first side is  8m  shorter  =  S - 8 .

The third side is  4 times as long as the first side =  4(S - 8) .

When you add up all three sides, you have 

                                           (S - 8)  +  (S)  +  4(S - 8)  .

That's a mess.
We need to clean it up.
Eliminate the parentheses:    S - 8    +    S    + 4S - 32 .

Add up all the S's:                  6S  - 8 - 32

Add up all the plain numbers:    6S - 40 .

That's the sum of all the sides.
Another name for it is 'perimeter'.
The question says it's  26m.
So we can write               6S - 40 = 26

Add  40  to each side:      6S        =  66

Divide each side by  6 :      S       =  11 m

First side      = S - 8    =   3 m
Second side = S         =  11 m
Third side     = 4(S-8) =  12 m