$\frac{3}{8} \times \frac{4}{11}=\cdots$

Step 1 ：Given the problem, we need to multiply the fractions \(\frac{3}{8}\) and \(\frac{4}{11}\).

Step 2 ：The rule for multiplying fractions is to multiply the numerators (the top numbers) to get the new numerator, and multiply the denominators (the bottom numbers) to get the new denominator.

Step 3 ：By multiplying the numerators 3 and 4, we get 12. By multiplying the denominators 8 and 11, we get 88. So, the result of the multiplication is \(\frac{12}{88}\).

Step 4 ：However, this fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 12 and 88 is 4.

Step 5 ：By dividing the numerator 12 by 4, we get 3. By dividing the denominator 88 by 4, we get 22. So, the simplified fraction is \(\frac{3}{22}\).

Step 6 ：Final Answer: \(\boxed{\frac{3}{22}}\)