To find 30 percent of 600, we can use the equation:
\[ \frac{30}{100} \times 600 \]
This can be simplified to find:
\[ 0.3 \times 600 = 180 \]
Now, let's evaluate the options given:
A. \(\frac{600 \times 6}{100 \times 6} = \frac{3600}{600}\)
- This simplifies to \(\frac{3600}{600} = 6\), which is not correct.
B. \(\frac{30 \times 6}{100 \times 6} = \frac{180}{600}\)
- This simplifies to \(\frac{180}{600} = 0.3\), which indicates that it represents 30 percent of 600. This is correct.
C. \(\frac{100 \times 20}{30 \times 20} = \frac{2000}{600}\)
- This reduces to \(\frac{100}{30}\) which is incorrect.
D. \(\frac{30 \times 1}{600 \times 1} = \frac{30}{600}\)
- This simplifies to \(\frac{1}{20}\) or 0.05, which is not the same as 30 percent of 600.
Therefore, the correct answer is B.