Woocommerce Shipping based on condition and cart value

Possible through backend, but you’ll have to use 2 shipping methods.

Flat rate with your shipping cost and free shipping with minimum order amount.

Adjust according to your zones.

Zone A:

http://puu.sh/tJDpg/be34c5739d.png

http://puu.sh/tJDsJ/7aae204650.png

And zone B will be just flat rate

Edit:

To hide other shipping methods when free shipping is available:

You’ll need to hook into woocommerce_package_rates.

Use one of the snippets in WooComm docs based on your version.

https://docs.woocommerce.com/document/hide-other-shipping-methods-when-free-shipping-is-available/