Decimal Movement in 512.4156: Positioning 6 in Hundredths Place

We are tasked with moving the decimal point so that '6' occupies the hundredths place. Here’s how we accomplish this:

• Currently, the number is 512.4156. The placement of digits relative to the decimal point is important.
• The '6' is initially the fourth digit to the right of the decimal:
  512.4156, where '6' is in the $10^{-4}$ place (ten thousandths place).
• The hundredths place is the second digit to the right of the decimal point.
• First, move the decimal from 512.4156 to 5124.156. This places '6' in the tenths place.
• Next, move the decimal again from 5124.156 to 51241.56. This sets '6' in the hundredths place.

Hence, we moved the decimal point 2 places to the right. The correct answer is $2$.