To solve this question, the user needs to know the concept of scientific notation. In scientific notation, a number is expressed as the product of a coefficient and a power of 10. The coefficient is a number between 1 and 10, and the power of 10 represents the number of places the decimal point must be moved to obtain the original number.

The notation -4e3 means -4 times 10 to the power of 3, or -4 multiplied by 1000. This gives us -4000.

Now, let's go through each option and explain why it is right or wrong:

A. -400: This option is incorrect because -400 is not equal to -4e3. A negative exponent in scientific notation represents a number less than 1, so -4e3 is a negative number with a large absolute value.

B. .004: This option is incorrect because .004 is not equal to -4e3. A positive exponent in scientific notation represents a large number, so -4e3 is a negative number with a large absolute value.

C. -4000: This option is correct. As explained earlier, -4e3 means -4 times 10 to the power of 3, or -4 multiplied by 1000. This gives us -4000.

D. .0004: This option is incorrect because .0004 is not equal to -4e3. A positive exponent in scientific notation represents a large number, so -4e3 is a negative number with a large absolute value.

Therefore, the answer is:

The Answer is: C