Listening to them deeply and finding out their core frustrations is key, just like how you would interact with a user to discover their pain points. In my experience, when my partner claims I work too much it isn't always because I literally work too much. Of course, sometimes my work/life balance needs to be readjusted and brought back to an acceptable equilibrium. However, the frustration often comes from not conve…
Having read the Love Languages book a while back, I'd point out that soupajoe's summary there at the end of his post is probably a good 95% of the value of the book. The book, IIRC, also suggests the idea that people have a "primary" language, and this is AIUI contested and in my opinion likely to be pop-sci nonsense. My wife scores highly on everything except gifts, which she thinks she likes in the abstract but tends to not really be that impressed when they manifest in the concrete. I suspect that many people have varying profiles that often resist being able to call one "primary", but the real point here is that it gives you a good set of five things to think about, discuss with your partner, and try out. (Because you have to bear in mind that humans are shockingly bad at guessing what will make them happy. That's a general rule, not a relationship rule. In particular that implies that you should not abandon one of the types until you have tried it, pretty much regardless of what your partner says. And, mutatis mutandis, regardless of what you say your partner should, ideally, try it anyhow to see how it goes.)
As another example, consider the idea that some people generally want to have their problems heard but don't want them "solved" in the conversation [1]. Regardless of whether or how true it may be in general, it again gives you a dimension to think about, consider with your partner, and experiment with, because in the end, everybody is their own person. My wife would clock in somewhere around 80/20; 80% she's just expressing herself and not looking for solutions, but maybe a fifth of the time she's at least open to thoughtful suggestions (as if nothing else it shows I'm fully engaged). Your mileage will vary.
And so on; rather than necessarily taking anyone's advice here directly, consider it a possible dimension to explore with your partner. With everything mentioned here you've probably got a good set of things to consider.
Further, for all of these things, you'll want to work out not only your partner's preferences, but your own, and some may surprise you even though you've lived with yourself for your entire life. Know thyself has been good advice for a very long time.