Choice B is correct. It’s given that the minimum value of $x$ is $12$ less than $6$ times another number $n$ . Therefore, the possible values of $x$ are all greater than or equal to the value of $12$ less than $6$ times $n$ . The value of $6$ times $n$ is given by the expression $6 n$ . The value of $12$ less than $6 n$ is given by the expression $6 n minus 12$ . Therefore, the possible values of $x$ are all greater than or equal to $6 n minus 12$ . This can be shown by the inequality $x \geq 6 n - 12$ .

Choice A is incorrect. This inequality shows the possible values of $x$ if the maximum, not the minimum, value of $x$ is $12$ less than $6$ times $n$ .

Choice C is incorrect. This inequality shows the possible values of $x$ if the maximum, not the minimum, value of $x$ is $6$ times $n$ less than $12$ , not $12$ less than $6$ times $n$ .

Choice D is incorrect. This inequality shows the possible values of $x$ if the minimum value of $x$ is $6$ times $n$ less than $12$ , not $12$ less than $6$ times $n$ .