Please note: This platform is to help you with your code/errors you're facing and not to spoon-feed you.

Now coming to your question

const db = require('quick.db')
client.on("messageCreate", async message => {
    if (message.content.startsWith('!blacklist')) {

        let mentions = message.mentions.users.first()
        if (!mentions) {
            return message.reply({ content: `Please mention a user!` })
        } else {
            await db.push(`_blacklisted_`, mentions.id)//Including the mentioned member into the blacklisted list
            message.channel.send({ content: `Blacklisted **${mentions.tag}**` })
        }
    }
    if (message.content.startsWith('!whitelist')) {
        let mentions = message.mentions.users.first()
        if (!mentions) {
            return message.reply({ content: `Please mention a user!` })
        } else {
            let check_blacklist = await db.get(`_blacklisted_`, [])
            let index = check_blacklist.indexOf(mentions.id)
            if (index > -1) {
                check_blacklist.splice(index, 1)//remove the mentioned user from the blacklisted array
                await db.set(`_blacklisted_`, check_blacklist) //Setting the new list
                message.reply({ content: `Whitelisted ${mentions.tag}` })
            } else {
                message.reply({ content: `${mentions.username} is not blacklisted` })
            }

        }

    }
})

Do read the docs