To solve for \( f \) in the equation
\[ 2 - \frac{1}{4}f = f - \frac{3}{4}f + 3, \]
first simplify the right side:
\[ f - \frac{3}{4}f = \frac{4}{4}f - \frac{3}{4}f = \frac{1}{4}f. \]
Now, replace that in the equation:
\[ 2 - \frac{1}{4}f = \frac{1}{4}f + 3. \]
Next, get all the terms involving \( f \) on one side and constant terms on the other side. First, add \( \frac{1}{4}f \) to both sides:
\[ 2 = \frac{1}{4}f + \frac{1}{4}f + 3. \]
This simplifies to:
\[ 2 = \frac{2}{4}f + 3. \]
Now simplify \( \frac{2}{4}f \) to \( \frac{1}{2}f \):
\[ 2 = \frac{1}{2}f + 3. \]
Next, subtract 3 from both sides:
\[ 2 - 3 = \frac{1}{2}f, \]
which simplifies to:
\[ -1 = \frac{1}{2}f. \]
Now, multiply both sides by 2 to solve for \( f \):
\[ f = -2. \]
Thus, the solution is:
\[ \boxed{-2}. \]