Once you subtract 27 from both sides, what simpler equation involving $6m$ do you get?

When you have an equation of the form $6m = 36$, what operation will isolate $m$?

After doing the algebra yourself, you should have $m$ written as a division expression. In Desmos, type (63 - 27) / 6 into an expression line and let Desmos compute the value of this expression; that value is the solution for $m$.

Start with the equation $6m + 27 = 63$. To isolate the term with $m$, subtract 27 from both sides:

This simplifies to $6m = 36$.

Now you have $6m = 36$. To solve for $m$, divide both sides by 6:

This gives a simple division problem to simplify.

Compute $\dfrac{36}{6} = 6$, so $m = 6$.

Check: substitute $m = 6$ back into the original equation:

which matches the right side.

So the value of $m$ is 6, which corresponds to choice B.