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To solve the equation \( 3m + 54 - \frac{3m}{4} = -2 \), we will first eliminate the fraction by multiplying the entire equation by 4 (the denominator of the fraction). This gives us:
\[
4(3m) + 4(54) - 4\left(\frac{3m}{4}\right) = 4(-2)
\]
This simplifies to:
\[
12m + 216 - 3m = -8
\]
Next, we'll combine like terms on the left side:
\[
(12m - 3m) + 216 = -8
\]
This simplifies to:
\[
9m + 216 = -8
\]
Now, we will isolate \( m \) by first subtracting 216 from both sides:
\[
9m = -8 - 216
\]
This gives us:
\[
9m = -224
\]
Next, we divide both sides by 9:
\[
m = -\frac{224}{9}
\]
Thus, the value for \( m \) that makes the equation true is:
\[
\boxed{-\frac{224}{9}}
\]