What value will make the equation 3m+54−3m4=−2

To solve the equation \( 3m + 54 - \frac{3m}{4} = -2 \), we can follow these steps:

1. First, we can eliminate the fraction by finding a common denominator. The common denominator for 1 and 4 is 4. We can multiply every term by 4 to eliminate the fraction:

\[
4(3m) + 4(54) - 4\left(\frac{3m}{4}\right) = 4(-2)
\]

This gives us:

\[
12m + 216 - 3m = -8
\]

2. Now, combine like terms:

\[
12m - 3m + 216 = -8
\]

This simplifies to:

\[
9m + 216 = -8
\]

3. Next, we isolate \( m \) by subtracting 216 from both sides:

\[
9m = -8 - 216
\]

This simplifies to:

\[
9m = -224
\]

4. Finally, divide both sides by 9 to solve for \( m \):

\[
m = \frac{-224}{9}
\]

Thus, the value for \( m \) that makes the equation true is:

\[
\boxed{\frac{-224}{9}}
\]