Introduction:
To find the number by which we should multiply 2/11 to get -2/3, we need to apply the concept of multiplication of fractions. Multiplying fractions involves multiplying the numerators and denominators separately. In this case, we need to find the number that, when multiplied by 2/11, gives us -2/3 as the result.

Step 1: Write the given fractions:
Let's write down the given fractions:
2/11 and -2/3

Step 2: Set up the equation:
We can set up an equation to solve this problem. Let's assume the unknown number we need to find is represented by 'x'. So, we have:
2/11 * x = -2/3

Step 3: Cross-multiply:
To eliminate the fractions, we can cross-multiply the equation. This means we multiply the numerator of the first fraction with the denominator of the second fraction, and vice versa. So, we have:
2 * 3 = 11 * -2

Step 4: Solve for 'x':
Now, let's solve the equation to find the value of 'x'.
6 = -22

Step 5: Simplify the equation:
The equation 6 = -22 is not true because 6 is not equal to -22. This means that there is no number we can multiply by 2/11 to get -2/3.

Conclusion:
After solving the equation, we find that there is no number by which we can multiply 2/11 to get -2/3. Therefore, the answer to the question is that there is no solution.