We let $f_1, f_2, f_3$ and $f_4$ represent the number of fish she caught on the respective days. This means that $ f_1 + f_2 + f_3 + f_4 = 36 $. Further, we have that $ f_1 + 2 = f_2 - 2 = 2f_3 = f_4/2$.

From this last set of equations we can establish that

\[ \begin{eqnarray*} f_2 &=& f_1 + 4, \\ f_3 &=& \frac{f_1}{2} + 1, \\ f_4 &=& 4f_3. \end{eqnarray*} \]

First, we use these equations to eliminate $f_2$ and $f_4$ in the original equation.

\[ \begin{eqnarray*} f_1 + (f_1 + 4) + f_3 + 4f_3 &=& 36, \\ 2f_1 + 5f_3 + 4 &=& 36. \end{eqnarray*} \]

We now use the expression $f_3 = f_1/2+1$ from the first set of equations to substitute for $f_3$ in the last equation to get

\[ \begin{eqnarray*} 2f_1 + 5 \left(\frac{f_1}{2} + 1 \right) + 4 &=& 36, \\ 4f_1 + 5 f_1 + 18 &=& 72, \\ 9 f_1 &=& 54, \\ f_1 &=& 6. \end{eqnarray*} \]

Using back substitution gives $f_2=10, f_3 = 10$, and $f_4 = 16$.