Can I update my iPhone 6 to iOS 13 or later

You cannot pick and choose an iOS versions. What you get is Settings > General > Software update > [All options are available here]

You need to correctly Identify your iPhone model - Apple Support

These are the iOS options based on iPhone Model -->

• iOS 16.2 —>
  • Chipset A11 - 8 / 8 Plus / X
  • Chipset A12 - XR / XS / XS Max
  • Chipset A13 - SE (2020) / 11 / 11 Pro /11 Pro Max
  • Chipset A14 - 12 Mini / 12 / 12 Pro / 12 Pro Max
  • Chipset A15 - SE (2022) / 13 Mini / 13 / 13 Pro / 13 Pro Max
  • Chipset A16 - 14 / 14 Plus / 14 Pro / 14 Pro Max
• iOS 15.7.2 —>
  • Chipset A9 - 6S / 6S Plus /SE (1st Gen)
  • Chipset A10 - 7 / 7 Plus
• iOS 12.5.6 —>
  • Chipset A7 - iPhone 5S
  • Chipset A8 - iPhone 6/6 Plus
• iOS 10.3.4 —>
  • Chipset A6 - iPhone 5
• iOS 10.3.3 —>
  • Chipset A6 - iPhone 5C
• iOS 9.3.6 —> iPhone 4S - Chipset A5
• iOS 7.1.2 —> iPhone 4 - Chipset A4

Know how to...

• Update Over-the-Air (OTA) —> Update your iPhone or iPad - Apple Support (IN)
• Update using iTunes/Finder —> Update your iPhone, iPad, or iPod touch - Apple Support (IN)