You can use the following Bash script to handle web requests using only netcat (nc) and other commonly found binaries in BusyBox. This script will listen for incoming HTTP requests, send a "hello world" response for GET requests, and send a 405 "Method Not Allowed" error for all other request types. It will restart the nc process after every request.

```bash
#!/bin/sh

response_hello_world="HTTP/1.1 200 OK\r\nContent-Type: text/html\r\n\r\n<html><body><h1>Hello, World!</h1></body></html>"
response_method_not_allowed="HTTP/1.1 405 Method Not Allowed\r\nContent-Type: text/html\r\n\r\n<html><body><h1>405 Method Not Allowed</h1></body></html>"

while true; do
  rm -f request_pipe response_pipe
  mkfifo request_pipe response_pipe

  { nc -l -p 8080 < response_pipe 1> request_pipe & } 2>/dev/null
  nc_pid=$!

  read -r request_line < request_pipe
  method=$(echo "$request_line" | awk '{print $1}')

  if [ "$method" = "GET" ]; then
    echo -e "$response_hello_world" > response_pipe
  else
    echo -e "$response_method_not_allowed" > response_pipe
  fi

  # Wait for the nc process to finish and clean up
  wait $nc_pid
  rm -f request_pipe response_pipe
done
```

This script creates two named pipes (request_pipe and response_pipe) for communication with the nc process, listens on port 8080, and processes incoming requests accordingly. The script will keep running in a loop, restarting the nc process after each request.

Please note that this script is quite basic and may not handle all edge cases or follow best practices for production use. Consider using more mature web server software for real-world applications.
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