If the IPv6 field above stayed empty, it almost certainly means your internet provider hasn't turned IPv6 on for your connection yet — it is not a sign that something is broken, and there is usually nothing on your end that needs fixing. IPv6 has to be enabled at every step between your device and the wider internet, and providers have been rolling it out at very different speeds.
Where the gap usually is
IPv6 needs to work across your whole connection: your provider's network, the modem or router they gave you, and your device all have to support it at the same time. If any one of those three doesn't, you fall back to IPv4 only, and that's what you're seeing. In practice, the most common cause by far is simply that the provider's network doesn't offer IPv6 on your particular line yet, or offers it but hasn't switched it on for your account.
The situation in the Netherlands
Dutch providers have been rolling out IPv6 for years, but coverage is uneven — some connection types and regions have it, others are still waiting, and it isn't always switched on by default even where it's technically available. KPN, Ziggo and Odido have all made progress with IPv6 on parts of their networks, but "my provider offers IPv6 somewhere" and "my specific connection has it today" are not the same thing. If you want to check, your router's admin page will usually show whether it currently holds an IPv6 address, and your provider's support pages can confirm whether your connection type is covered.
Does it actually matter?
For almost everything you do day to day — browsing, streaming, messaging — no. Every major website works fine over IPv4, and your browser never bothers you about which one it used; that's the entire reason the checker on this page needed to tell you. IPv6 mainly matters if you do something that wants a direct, unshared connection to your device: hosting a game server, running remote access to a home NAS, or certain kinds of video calling and peer-to-peer software can behave better with it. If none of that describes you, missing IPv6 changes essentially nothing about your everyday internet.
Can you turn it on yourself?
Sometimes. If your router has an IPv6 setting that's simply switched off, turning it on can help — but if your provider's network doesn't offer IPv6 on your line at all, no router setting will conjure one up. The most reliable way to find out is to ask your provider directly whether IPv6 is available for your specific connection, since generic troubleshooting guides can't see your account.