1. The problem is to calculate the product $3 \cdot 6 \cdot 2 \cdot 4 \cdot \frac{1}{6}$.\n\n2. The formula for multiplication of numbers is simply multiplying all factors together: $$a \times b \times c \times d \times e$$\n\n3. Calculate step-by-step:\n$$3 \times 6 = 18$$\n$$18 \times 2 = 36$$\n$$36 \times 4 = 144$$\n$$144 \times \frac{1}{6} = \frac{144}{6}$$\n\n4. Simplify the fraction by canceling common factors:\n$$\frac{\cancel{144}}{\cancel{6}} = 24$$\n\n5. So, the final answer is $24$.