To simplify \(4 \frac{3}{4} - 6 \frac{1}{4}\), follow these steps:

1. Convert the mixed numbers to improper fractions:

- For \(4 \frac{3}{4}\):

\[
4 \frac{3}{4} = 4 + \frac{3}{4} = \frac{16}{4} + \frac{3}{4} = \frac{19}{4}
\]

- For \(6 \frac{1}{4}\):

\[
6 \frac{1}{4} = 6 + \frac{1}{4} = \frac{24}{4} + \frac{1}{4} = \frac{25}{4}
\]

2. Subtract the improper fractions:

\[
\frac{19}{4} - \frac{25}{4} = \frac{19 - 25}{4} = \frac{-6}{4}
\]

3. Simplify the fraction:

\[
\frac{-6}{4} = \frac{-3}{2}
\]

So, the correct simplified form is:

B. \(\frac{-3}{2}\)