The board is cut into two pieces: a short length and a long length. So we'll start by using the letter S to represent the short length and the letter L to represent the long length.
Let's write down what you know from the question:
The two boards together are 102", so S + L = 102.
The long piece is twice the length of the short piece: L = 2S
Now we take the first equation and replace L with what L is equal to (the second equation):
S + L = 102
S + ( 2S ) = 102.
Now can you solve the rest?