Duplicate the value of the price of the products to field in node I have node (Product display) and inside this node is field link to product. The usual option for commerce.

In commerce product is the field  - commerce_price. 

In node is field field_node_price.

How can synchronize value from commerce_price to field_node_price?
You need to use Computed Field here.


  Computed Field is a very powerful field module that lets you add a custom "computed fields" to your content types. These computed fields are populated with values that you define via PHP code. You may draw on anything available to Drupal, including other fields, the current user, database tables, you name it. (Feeling the power yet? :) ) You can also choose whether to store your computed field values in the database with other content fields, or have them "calculated" on the fly during node views. (Although you should note that Views use requires database stored values.) This field is literally the Swiss Army knife of fields. So start cooking up your PHP based values!


Now, substitute plain link with Entity reference - that way you will be able to access referenced product's fields in code and use them, especially price, in node's computed field