Question: I am trying to make a monster farm and I’m worndering if there is a certain distance needed between spawners

Answer: 
According to the wiki, it says "A spawner activates when a player comes within a spherical radius of 16 blocks from the center point of the block; i.e. 15.5 blocks from the block itself."Which means that you have to be 15.5 or fewer blocks away from the spawner in order to for the spawner to activate and spawn mobs.
It will spawn mobs if the player is within a 8\*8\*3 radius of each spawner