To solve the equation \( \frac{1}{4}b - 2 = -\frac{1}{2}b + 4 \), we will first eliminate the fractions by finding a common multiple of the denominators. The common denominator for 4 and 2 is 4.
- Multiply the entire equation by 4 to eliminate the fractions:
\[ 4 \left( \frac{1}{4}b \right) - 4(2) = 4\left(-\frac{1}{2}b\right) + 4(4) \]
This simplifies to:
\[ b - 8 = -2b + 16 \]
- Next, add \( 2b \) to both sides to get all \( b \) terms on one side:
\[ b + 2b - 8 = 16 \]
This simplifies to:
\[ 3b - 8 = 16 \]
- Now, add 8 to both sides to isolate the \( b \) term:
\[ 3b = 16 + 8 \]
This simplifies to:
\[ 3b = 24 \]
- Finally, divide both sides by 3 to solve for \( b \):
\[ b = \frac{24}{3} \]
This simplifies to:
\[ b = 8 \]
Thus, the solution is:
\[ \boxed{8} \]
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