You don't have to show personal experience. The idea is to show support for why your answer is a solution to the OP's problem
Not all questions are asked in the same mode, and not all types of answers are equally appropriate for all questions.
A question like "how will it affect a combat if I add +2 AC to this monster against this particular party?" can probably be answered adequately with math: you can look at the probability distributions for attack rolls hitting the original AC and the modified AC and extrapolate that a combat will probably last X-Y rounds longer, subjecting the PCs to Z additional risk of hitpoint loss, or something along those lines. In this case the math may be enough support for an answer.
A still better answer might fold in personal experience as well. Whether or not the math is included, something like "when the AC gets as high as +2 would grant this creature, my players usually switch from a fighter-focused, attack-based strategy with spellcaster support to a spellcaster-focused, save spell-based strategy with fighter support. This made combat shorter and easier, though the PCs used more of their limited resources for the day on spells." In this case the personal experience is the support for the answer: it describes what happened when the +2 AC was attempted.
Both of these are answers that I, personally, would accept as sufficiently supported (for this very contrived example, at least). They include advice as well as an explanation for why that advice is appropriate, applicable, and valuable. These features tend to make answers better and also make it possible to judge between different answers.
The linked question is not an ideal one
The headline is asking for something subjective: what makes a combat interesting. The body of the question is better, asking about making combats more challenging, but that is still not all that well-defined.
Answering such a question directly is very difficult in the SE mode, and that is almost certainly the reason the question was closed. The issue then becomes one in which support for an answer is difficult because the question itself is at odds with how the stack is intended to work. If a question isn't really answerable in the SE way then the most appropriate course of action is to adjust the question rather than to write looser answers. Even with that in mind there is considerable wiggle room on the matter, but if you choose to answer a more marginal question you'll have more openings for critiques.
The linked answer lacks much support of either type
There is neither math nor personal experience in it. It essentially says "you can add more things to combats to make them interesting. Here are some things: [...]". Traps are mentioned, for example, but there is no description of what kinds of traps make combats more interesting, or in what way, or what circumstances traps work particularly well or poorly in, nothing about how to calibrate them, how the kobolds might lead the party towards the traps, or anything else. A later edit added in some information along these lines but is still pretty thin in my reading, but is better than the version of the answer that did not have that experience. The edited version provides some additional guidance beyond "do something".
A good answer to a good question is directly usable in some fashion
As above, the question is not ideal as currently written-- if the players in that game find traps boring and irritating then traps in combat is not a good solution to the problem, which is why "interesting" is not really an appropriate goal for an SE question. "Challenging" is better, but (continuing with the trap example) that doesn't provide enough information to choose a specific trap or calibrate one for an encounter. But even if it were, the linked answer doesn't clearly identify what makes its suggestions appropriately challenging in a way that solves the querent's problem. This is true even though they're good ideas-- they just lack the necessary details to be translated into a specific game in a way that precisely addresses the question.
tl;dr: the best answers don't slavishly have support in exactly form X; they have support appropriate to the suggestions they make in service of answering the question as directly and fully as possible.