How to derive the reaction function from these provided variables?
The reaction function tells you how a player in a game reacts to the strategy of another player.

As noted by denesp in the commentary, the statements provided in the question are verbal descriptions of reaction functions. The mathematical description (in millions) is given as follows:

Firm 1:
$x_1= 2 + (1/3) x_2$

Firm 2:
$x_2= 7 + (1/8) x_1$

There is not really any procedure to it, besides rewriting the verbal description into a mathematical description.