\cos\left(-\frac{4\pi}{6}\right)=\cos\left(\frac{4\pi}{6}\right)=\cos\left(\frac{2\pi}{3}\right)=\cos\left(\pi-\frac{\pi}{3}\right)=\cos\pi\cos\left(\frac{\pi}{3}\right)+\sin\pi\sin\left(\frac{\pi}{3}\right)=-\cos\left(\frac{\pi}{3}\right)