0.6x7=4.2, so 4.2 is a multiple of 0.6, and 0.6 is a multiple of 4.2. Is this correct? Tell me why.

This conclusion is wrong. The multiplication operation is in the integer range. An integer can be divisible by another integer, which is a multiple of another integer. For example, 6 can be divisible by 2 or 3, so 6 is a multiple of 2 and 3. 0.6×7=4.2, we can only say that 4.2 is 7 times of 0.6, but we can't say that 4.2 is a multiple of 0.6, because neither 4.2 nor 0.6 is an integer. How many times cannot be an integer, and multiples must be within the integer range. It is right that 0.6 is a factor of 4.2, because two numbers are multiplied, one of which is a product factor, and these two numbers may not be integers.