Question

how do I know if they are real numbers
?
Solve.

4(a + 3) = 12 + 4a

Answer 1

what you mean is "how do you know if the solutions is ALL REAL NUMBERS ?

Answer 2

and you know that because if you multiply out on the left, you get
\[4a+12\] by the distributive property, which is identical to the expression on the right of the equal sign

Answer 3

in other words, you are looking at \[4a+12=4a+12\] which is pretty clearly an "identity" true for all real numbers