If I need to use an 8-8-8 fertilizer stick to fertilize the soil around my pomegranate tree, can I use, let's say, four 2-2-2 fertilizer sticks to amount to the proper 8-8-8 npk ratio?
The simple answer is yes, 4 2-2-2 sticks will be about equal to 1 8-8-8 stick. But as you get deeper into gardening, you'll find that most experienced folk are not using fertilizer sticks. You'll probably be happier with your results if you study a bit more deeply about fertilizer, how to use it, and what might be important things to know regarding the fertilization of the crop or crops you're raising.
A big problem with fertilizer sticks is that nutrients tend to stay in the vicinity of the sticks rather than move throughout the soil area. Dry fertilizer pellets or grains sprinkled on the surface, or mixed with water and poured over the entire surface are generally more effective. Also, another factor to consider is the pH of the soil you have. Pomegranate likes an alkaline environment, pH 7.5 - 8.0; you can have a soil test done at the county extension service, which will tell you if you need to add some lime to your soil. This link will help you find the nearest office:
Also, an equalized NPK ratio (1-1-1) is not necessarily the best. For instance, plants actually use the major nutrients in a 3-1-2 ratio, which is increasingly easy to find. Also you need micronutrients in the mix also, if you're going to have a good fertilizer. These articles should be useful: https://www.gardeningknowhow.com/edible/fruits/pomegranate/no-pomegranates-on-trees.htm