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Hi !
To get the same answer, you need a specefic formula that you can find by following this link :

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The link is in french, but you just need to look at the formula :
$$g=\frac{G\cdot m}{r^2}$$
In this case, the only thing you need to know is that \(r\) is the distance between the core of the planet and the altitude. Knowing that we're comparing to point for the same planet, \(G\) and \(m\) are the same. Now you can calculate the \(g\) for each situation. The first one is at the surface :
$$g_1=\frac{G\cdot m}{r_1^2}$$
The second situation will be like this :
$$g_2=\frac{G\cdot m}{r_2^2}$$
If you try to put the first formula in the second one (replace \(G\cdot m\)), you will get this :
$$G\cdot m=\frac{g_1}{r_1^2}$$
$$g_2=\frac{\frac{g_1}{r_1^2}}{r_2^2}=\frac{g_1}{r_1^2\times r_2^2}$$
We know that \(g_1\) is 9.8, but we don't know the value for \(r_1\) and \(r_2\). We will assume that \(r_1\) is equal to one. This means that \(r_2\) is equal to 4 :


You can now enter the values to obtain this final form :
$$g_2=\frac{9.8}{(1)^2\times (4)^2}=\frac{9.8}{(4)^2}$$
It gives you the same answer than your notes ! If you have any other questions, do not hesitate !