This problem is modeled as a bipartite graph.
We have,
$$\begin{align*} &\Rightarrow \sum d_i = 2E \\ &\Rightarrow {\color{red}{\sum d_{x_i}}} + {\color{blue}{\sum d_{y_i}}}= 2E \\ &\Rightarrow {\color{red}{\sum d_{x_i}}} + {\color{blue}{\sum d_{y_i}}} = 2.{\color{red}{\sum d_{x_i}}} \\ &\Rightarrow {\color{blue}{\sum d_{y_i}}} = {\color{red}{\sum d_{x_i}}} \\ &\Rightarrow {\color{blue}{\sum_{\;}^{4n} d_{y_i}}} = \left ( 4n^2 \right )_{\text{min}} \\ &\Rightarrow 4n.\left ( d_{\text{people}} \right )_{\text{average}} = \left ( 4n^2 \right )_{\text{min}}\\ &\Rightarrow \left ( d_{\text{people}} \right )_{\text{average}} = n_{\text{min}} \\ \end{align*}$$
$$\begin{align*} &\Rightarrow \exists y \in {\text{\{People\}}} \text{ such that } d_y \geq n \\ \end{align*}$$