To solve the problem \( \frac{42}{3} \times \frac{3}{7} \times \frac{2}{6} \), we will follow these steps:
### Step 1: Rewrite the fractions
We can rewrite the fractions as:
\[
\frac{42}{3} \times \frac{3}{7} \times \frac{2}{6}
\]
### Step 2: Simplify \( \frac{42}{3} \)
Calculate \( \frac{42}{3} \):
\[
\frac{42}{3} = 14
\]
### Step 3: Rewrite the remaining fractions
Now, we rewrite the remaining fractions:
\[
14 \times \frac{3}{7} \times \frac{2}{6}
\]
### Step 4: Simplify \( \frac{3}{7} \) and \( \frac{2}{6} \)
We can simplify \( \frac{2}{6} \) to \( \frac{1}{3} \):
\[
\frac{2}{6} = \frac{1}{3}
\]
Now we can rewrite the expression:
\[
14 \times \frac{3}{7} \times \frac{1}{3}
\]
### Step 5: Cancel out \( 3 \) in \( \frac{3}{7} \) and \( \frac{1}{3} \)
The \( 3 \) in \( \frac{3}{7} \) and \( \frac{1}{3} \) can be canceled:
\[
14 \times \frac{1}{7}
\]
### Step 6: Calculate \( 14 \times \frac{1}{7} \)
Now we can calculate:
\[
14 \times \frac{1}{7} = \frac{14}{7} = 2
\]
### Step 7: Final multiplication with remaining fractions
Now we multiply by the remaining fractions:
\[
2 \times 1 = 2
\]
### Final Answer
Thus, the product is:
\[
\boxed{2}
\]
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