Radix-2 vs Radix-4 FFT
The reason the Radix-4 FFT is of interest is in the simplicity of multiplying by $\pm j$ in actual implementation. Below shows the Radix-4 4 point DFT core processing element as part of the Radix-4 FFT Butterfly in comparision to the Radix-2 FFT butterfly (with 2 point DFT core processing element) and the resulting decrease in number of operations, applicable when the input signal is of a length that is a power of 4 (or for portions of the signal that are).



To further see how the radix-4 algorithm reduces multiplications consider the number of real multipliers and additions in a complex multiplier:
$$V_1V_2 =  I_{out}+jQ_{out}= (I_1+jQ_1)(I_2+jQ_2) = (I_1 I_2 - Q_1 Q_2) + j(I_1Q_2+I_2Q_1)$$
Where we see from above there are 4 real multipliers and 2 additions (Where the real and imaginary components are maintained on separate paths so not actually added).
Now consider if $V_2$ above was $j$, then $I_2 = 0$ and $Q_2 = 1$:
$$V_1V_2 =  V_1j = (I_1 0 - Q_1 1) + j(I_1 1 +0 Q_1) = -Q_1 + jI_1$$
We see that multiplying a complex number $I_1+jQ_1$ by $j$ is done by simply changing the sign of $Q$ and then swapping $I$ and $Q$. Similarly multiply by $-j$ would be done by changing the sign of $I$ and then swapping $I$ and $Q$.
The radix-4 allows for an increased number of multiplications by $\pm j$ where the radix-2 solution minimizes all complex multiplications including multiplying by $\pm j$.