In John 6, Jesus had just declared himself to be the "bread of life" that came down from heaven. Many of the people listening, particularly the Jews, were skeptical and started grumbling and murmuring amongst themselves. They questioned how Jesus could claim to have come from heaven, as they knew his parents, Mary and Joseph.

Therefore, when Jesus says "Don't murmur among yourselves," he is addressing their internal complaints and doubts. Here's a breakdown of what it means:

"Murmur": This refers to a low, indistinct complaining, often done privately or in small groups. It suggests discontent, dissatisfaction, and a lack of open or respectful discussion. In this context, it implies they were doubting and criticizing Jesus amongst themselves, rather than openly asking him for clarification.

"Among yourselves": Jesus is specifically addressing the fact that they are not confronting him directly with their questions or doubts, but instead, spreading negativity among themselves.

In essence, Jesus is telling them to:

Stop being skeptical and doubting him in secret.
Address their concerns openly and honestly.
Instead of spreading negativity, seek understanding.
Open dialogue is preferable to quiet grumbling.

The verse suggests that Jesus preferred honest doubt and questioning over passive-aggressive discontent that spread through the crowd, preventing genuine faith and understanding. It is an instruction to engage with him and his teachings with an open mind instead of allowing preconceived notions to lead to secret disapproval.