All these four words 多亏, 幸亏, 幸好 and 好在 can be used for a situation: due to some favorable conditions, bad results are avoided. How to differentiate between them?
“多亏” is a verb and “幸亏、幸好、好在” are adverbs. “幸亏、幸好、好在” have very similar meanings and generally can be used interchangeably.
多亏
It is a verb, and often followed by someone or someone’s help thanks to which something bad or negative is avoided. It is used with a grateful tone.
E.g.
多亏近来的研究才有了有效的疗法。Thanks to recent research, effective treatments are available.
多亏了这些练习我通过了考试。I have passed the exam thanks to the exercises.
幸亏, 幸好
Due to accidental/coincidental causes, something negative or unfortunate does not happen, something positive or fortunate happens, or someone is lucky enough to escape a trouble or disaster. Both are used with a very lucky and fortunate tone.
E.g.
幸亏/幸好你及时帮忙，我们才按时完成了任务。It was thanks to your timely help that we accomplished the task on time.
我幸亏/幸好选择得对，结果赢了！I made a fortunate choice and won!
幸亏/幸好你带了伞，开始下雨了。It’s a good job you brought your brolly, it’s starting to rain.
好在
Often used to mean that something negative or unfortunate happens, but luckily or fortunately the situation is not that bad/serious.
E.g.
好在他伤势不重。Luckily he was not very seriously wounded.
他出了车祸，好在只是擦破了一点皮。He had an accident, but fortunately it’s only a scratch.
学费的筹措可能看似一个大难题，好在你可以获得许多帮助。Financing your studies may seem like a tall order, but there is plenty of help available.
Case in which only “多亏” can be used：
⭐️⭐️⭐️⭐️⭐️ When used in this formula “多亏了 + object”, “多亏了” can’t be replaced by the other three.
E.g.
多亏了你，工作很快就完成了。
Thanks to you, I finished the work quickly.
多亏了他的帮助，我成功地完成了这个项目。
Thanks to his help. I finished it successfully.
It is a verb, and often followed by someone or someone’s help thanks to which something bad or negative is avoided. It is used with a grateful tone.
多亏了及时雨，农民们有了好收成。
Thanks to the timely rain, the farmers had a good harvest.
Case in which “多亏、幸亏、幸好、好在” can be used interchangeably
⭐️⭐️⭐️⭐️⭐️ When used in this formula “多亏（了）+ a short sentence”, “多亏、幸亏、幸好、好在” can be used interchangeably, but “多亏” expresses more a grateful tone, and “幸亏、幸好、好在” more a fortunate tone.
E.g.
多亏及时送医院， 再晚半小时他就没希望了。（4）
Fortunately he was sent to the hospital in time. If he had been delayed half an hour, he would have not been still alive.
大楼突然起火了，多亏（了）消防员及时赶到，很快就把火扑灭了。（5）
The building burst into flames, thanks to the firefighters timely arrival, the fire were put out very soon.