To get the big map value from a smart contract using Taquito, you need to first get the contract address and then use the Tezos.contract.at() method to get the contract instance. You can then use the contract.storage() method to get the storage and then use the PROPERTY.get() method with the key to get the corresponding value. If you are getting any error, it is best to provide more information about the error so that we can help you troubleshoot it.