Is the product of a 4 digit number and 2 digit number always a 6 digit number?

The smallest 4 digit no is 1000. The smallest 2 digit no. is 10. Multiply these, you get 10,000. this is a 5 digit no. so the answer to your question is no. Multiplying one thousand by ten to get ten thousand is something you can do in your head in much less time than sending a question to wiki-answers. If you want to get better at math, start by always spending half a minute in thinking "is there an easy way to do this".