According to the given data we have the following:
1.The fact that 2(x + 3) = 2x + 6 is attributable to the Blank Property.
In this case the fact that 2(x + 3) = 2x + 6 is attributable to the distributive property. This is because if you multiply 2 times x and 3 you will get the 2x and 6.
When you multiply a number and a variable, you can just write them side by side to express the multiplied quantity.
2. The fact that 3x = 0 implies that x = 0 is a result of the Blank Property.
In this case this is a result of the zero product property, which means that if the product of two terms is 0, then one of the factors must be 0.