<p>We investigate theoretically the improvement of the entanglement between the indirectly coupled two magnon modes in a magnomechanical system with magnon squeezing. We quantify the degree of entanglement via logarithmic negativity between two magnon modes. We show a significant enhancement of entanglement via magnon squeezing. Additionally, the entanglement of two magnons decreases monotonically under thermal effects. We demonstrate that with an increasing photon tunneling rate, entanglement is robust and resistant to thermal effects. We use purity as a witness to the mixing between the two magnon modes. We show that synchronization and purity are very robust against thermal effects rather than entanglement. We examine the relationship between quantum entanglement, purity, and quantum synchronization in both steady and dynamic states. According to our results, this scheme could be a promising platform for studying macroscopic quantum phenomena.</p>