Let's break this down, step-by-step:
A 216-inch board is cut into two pieces: this is our total length
one piece is five times: let's call the length of this piece 5x, where x is the length of the other piece
the length of the other: this is the length of our shorter piece, which we've decided to give a value of x
find the lengths of the two pieces:
If the total length of the two pieces is 216 inches, then we need to add 5x, the length of our longer piece, to x, the length of our shorter piece, to get 216 = 5x + x.
We combine like terms to get 216 = 6x
Divide both sides by 6 to isolate the variable: 216 ÷ 6 = x
The length of the shorter piece is x = 19 inches
The length of the longer piece is 5x = 95 inches
We can check our work: 114 = 19 + 5(19) = 114 inches.