How should I calculate the values of a and b when a(4x+12) is equivalent to 2x+36b?

Firstly, start off by expanding the brackets on the left hand side of the equation

a(4x+12) would expand as below:
4x multiplied by a gives 4ax12 multiplied by a gives 12a

We now know that 4ax is the equivalent of 2x, so we can go on to work out the value of a.

If we remove the constant x, we get 4a is equal to 2. Therefore, if you do 2/4, you get the value of a - in this case, you can simplify 2/4 to 1/2

Therefore, a=1/2

So now that we know a is equal to one half, we can now calculate the value of 12a, which is equal to 6.

As a result of knowing that 12a is equal to 6, we now know that 36b is also equivalent to 6.

We can work out the value of b by dividing 6 by 36, to get 6/36 as the value of b. We can further simplify this to 1/6 as the value of b.

Therefore, we know that the answers are:
a = 1/2
b= 1/6

It is okay to leave the answers as a fraction, as this tends to be more accurate than using decimal places. However, always check to see whether the question requires the answer a certain way.