$\displaystyle \frac{b}{d} = 1$ means that $\displaystyle b = d$

Therefore, the function becomes :

$\displaystyle f(x)=\frac{2x+b}{cx+b}$

Now you know that $\displaystyle \frac{ -4}{3} c + d = 0$ , which means that $\displaystyle c = \frac{ 3d}{4}$

Therefore, the function becomes :

$\displaystyle f(x)=\frac{2x+b}{\frac{ 3d}{4} x+b}$

Remember that $\displaystyle b = d$, so we have :

$\displaystyle f(x)=\frac{2x+b}{\frac{ 3b}{4} x+b}$

Now use one of the x-axis / y-axis values to substitute, isolate and solve $\displaystyle b$.

You can solve for $\displaystyle b$, therefore you can solve for $\displaystyle d$, and the last variable remaining ($\displaystyle c$) can be found by reverting to the original function and substituting the y-axis cut values.

I might have done some errors in the spoiler though, so don't just copy blindly.