**The product of 2 and 4 square root of 2 is 11.313708499, or 11.31 if rounded to nearest hundredths.** The key to solving this problem is to know the correct order of operations, "PEMDAS" for parentheses, exponents, multiplication/division and addition/subtraction, and how to get the square root of a number.

The first thing to do is get the square root of 2; this operation falls under exponents. This step consists of determining what number when raised to the 2nd power results in 2. The answer is 1.4142135623730950488016887242097.

The operation between the given numbers is multiplication. The flow of solving must be from left to right: 2 x 4 x 1.4142135623730950488016887242097, thus giving us the final product of 11.313708499.