1. The problem is to evaluate the expression $5:2:4 \div 5:4:6$. Here, the colon ":" is interpreted as division, so the expression can be rewritten using division symbols. 2. Rewrite the expression: $$\frac{5}{2} \div 4 \div \frac{5}{4} \div 6$$ 3. Division is performed from left to right, so first calculate $\frac{5}{2} \div 4$: $$\frac{5}{2} \div 4 = \frac{5}{2} \times \frac{1}{4} = \frac{5}{8}$$ 4. Next, divide the result by $\frac{5}{4}$: $$\frac{5}{8} \div \frac{5}{4} = \frac{5}{8} \times \frac{4}{5} = \frac{20}{40} = \frac{1}{2}$$ 5. Finally, divide by 6: $$\frac{1}{2} \div 6 = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}$$ 6. Therefore, the value of the expression is $\frac{1}{12}$.