To solve multiplication problems using place value and regrouping, we break down the numbers into their individual place values (ones, tens, hundreds, etc.). In this case, we first multiply the digit in the ones place (8) by 6, which results in 48. Since 48 is greater than 10, we write down 8 and carry over 4 to the next place value (tens). Next, we multiply the tens digit (7) by 6, which gives us 42. Adding the carried over 4 gives us 46, so we write down 6 and carry over 4 again. Finally, we multiply the hundreds digit (3) by 6, resulting in 18, and adding the carried over 4 gives us 22. We write down 2 and carry over 2 to the thousands place. This process of carrying over occurs whenever the product of a multiplication exceeds 10, indicating that we need to regroup into the next higher place value.