Both of your answers are correct!
To clarify your first equation for other readers: "three less than a number" means the number minus 3, so - 3 will be at the end of the equation. "A number multiplied by 6" means the number times 6. Choose any symbol to represent "a number." Grace chose x as the symbol. So, the expression becomes 6x - 3.
The 2nd equation is an example of using the distributive property to solve a problem.
For 1*(3+7), you multiply 1 by the first term in the parentheses (1*3), then by the second term in the parentheses (1*7). Put a plus sign between the two because there is a plus sign inside the parentheses. So, 1*(3+7) = (1*3) + (1*7). If there had been a minus sign inside the parentheses, there would be a minus sign between the two products. 1*(3-7) = (1*3) - (1*7)
Grace, it looks like you have a good handle on your math!