why am i getting an error code 4010

To update iOS your device needs to verify the credentials through Apple Update servers. If you do not have a stable internet connecrtion this verification process may not get completed.

It would be better if you can please re-post with a screenshot, in order to understand the phenomenon better. Images/pictures speak louder than words. 

Please understand this is a public forum: While attaching a Screenshot, do not provide any personal credentials, such as IP address, Card detail, email id, apple id, IMEI number, Serial Number, Phone number, Order ID, if you are sharing a map ensure your location is not identifiable, etc.

Sometimes, simply restarting your iPhone can resolve issues with software updates.

1. Restart the device. That's it.
2. Still not solved --> Force restart iPhone - Apple Support

Check your internet connection:

Connecting to Wifi is the first part and then getting connected to the Internet is the second

1. If you connect to Wifi, doesn't necessarily mean you are connected to the internet. If you are not connected to wifi could be a problem with iPhone settings or Router/Modem Settings
2. If you are not connected to the internet is the sole issue of Router / Modem Settings. Contact your ISP immediately

Check your WiFi Router / Modem for --> Recommended settings for Wi-Fi routers and access points ...

For your Internet connection.

• Over Cellular: contact your Carrier (Cellular Service Provider). The agency who issued the SIM to you
• Over WiFI: Contact your ISP (Internet Service Provider), the agency who provided the Internet Service on your Modem/Router to you

However --> Connect iPhone to the Internet - Apple Support

Update using iTunes: you need to update your device with iTunes.