As long as you have your seed phrase or the private key, you can access your MetaMask Extension account on any device. But, in the absence of a private key, this task could not be completed even if you do remember your MetaMask password. So, before you initiate this process, make sure you have access to the secret recovery phrase and then go ahead with applying the steps listed right here in this post.
Accessing the same MetaMask wallet on another device could be a sheer necessity when you have forgotten your device back at someplace and you could not be physically present there to access your wallet. So, in that case, what you can do is import the wallet on another device after making sure that you have your 12-word secret recovery phrase with you.