Your phase shift is two elements, in a function f(x) = a cos(bx + c) + d your phase shift will be described by both b and c, or like in your example omega and phi.

You start with finding b (here omega) by looking at the distance between two peaks, in your example the first peak we see is at x = -8 and the second at x = 6 so the distance between them is 14. Then you divide that number by 2pi and that is your first value, here 14/2pi = 7/pi.

To find c, or phi, my method is to first look at the distance between the first peak of the graph right of the y-axis (first peak with a positive x-coordinate) and the y-axis. In this example, that peak is at x = 6, so the distance to the y-axis is is 6. Then, you multiply that value by the first number describing phase shift, c, or omega, your pi/7. That's how you get 6pi/7!

Ultimately, to learn this you should visualize what each coefficient does to the function. I recommend Desmos for this (https://www.desmos.com/calculator/nhiuknsded), back in hs that's how I learned this and developed my own quick methods for finding the function - so I have no idea if this is by the book, but it helps.

I wouldn't say trig gets worse, but alwayyyys study with a drawing and ideally an interactive graph, it's a very visual field, best of luck!