1. The problem involves comparing the fractions $\frac{3}{6}$, $\frac{6}{10}$, and $\frac{9}{12}$.\n\n2. To compare fractions, we can simplify each fraction to its lowest terms or convert them to decimals.\n\n3. Simplify $\frac{3}{6}$: both numerator and denominator can be divided by 3.\n$$\frac{\cancel{3}}{\cancel{6}} = \frac{1}{2}$$\nSo, $\frac{3}{6} = \frac{1}{2} = 0.5$.\n\n4. Simplify $\frac{6}{10}$: both numerator and denominator can be divided by 2.\n$$\frac{\cancel{6}}{\cancel{10}} = \frac{3}{5}$$\nConvert $\frac{3}{5}$ to decimal: $\frac{3}{5} = 0.6$.\n\n5. Simplify $\frac{9}{12}$: both numerator and denominator can be divided by 3.\n$$\frac{\cancel{9}}{\cancel{12}} = \frac{3}{4}$$\nConvert $\frac{3}{4}$ to decimal: $\frac{3}{4} = 0.75$.\n\n6. Now compare decimals: $0.5$, $0.6$, and $0.75$.\n\n7. Therefore, $\frac{3}{6} < \frac{6}{10} < \frac{9}{12}$.\n\n8. The shaded bar graphs visually represent these fractions: 3 out of 6 sections, 6 out of 10 sections, and 9 out of 12 sections filled, matching the fractions given.