Does the 11.6 update fix the slowness of my iphone after updating 11.2?

There is no 11.6 update.

If you mean 11.2.6, the answer is no. It's not meant to.

About iOS 11 Updates - Apple Support

iOS 11.2.6 includes bug fixes for your iPhone or iPad. This update:

• Fixes an issue where using certain character sequences could cause apps to crash
• Fixes an issue where some third-party apps could fail to connect to external accessories

For information on the security content of Apple software updates, please visit this website: https://support.apple.com/kb/HT201222

So check out the suggestions for speeding up your iPhone here.