Keksimme paremman tavan säästää energiaa.

It comes from the verb keksiä. In this sentence, it means something like to come up with, to think up, or to find/invent an idea or solution.

So keksimme paremman tavan is not necessarily about inventing a physical object. It more naturally suggests we came up with a better way or we found a better method.

It can be either one, depending on context.

For keksiä, the form keksimme can mean:

• we come up with / we invent
• we came up with / we invented

Finnish has some verb forms that look the same in the present and the past. Usually the surrounding context makes the meaning clear.

Because the ending -mme already tells you the subject is we.

• keksin = I come up with
• keksit = you come up with
• keksimme = we come up with / came up with

Finnish often leaves out subject pronouns when they are not needed. You could say Me keksimme..., but that usually adds emphasis, like we did it.

That is exactly what it is. Finnish comparison is irregular here:

• hyvä = good
• parempi = better
• paras = best

So paremman is a case form of parempi.

In other words:

• base comparative: parempi = better
• here: paremman because the adjective has to match the case of tavan

Because paremman tavan is the object of the verb keksimme.

The basic dictionary forms are:

• parempi tapa = a better way

But in this sentence, Finnish uses the total object form for one complete thing that was thought up/found. In the singular, that form usually looks like the genitive:

• parempi tapa → paremman tavan

The adjective must agree with the noun, so both words change:

• parempi → paremman
• tapa → tavan

This is the required case form here, and it also shows consonant gradation.

• basic form: tapa
• changed form: tavan

The p becomes v in this form. That is a normal pattern in Finnish for many words.

So the change is not random: it is part of how the word behaves when inflected.

Säästää is the first infinitive, the basic verb form you learn in the dictionary. It corresponds to English to save.

After tapa meaning way/method, Finnish commonly uses this structure:

• tapa tehdä jotain = a way to do something

So:

• tavan säästää energiaa = a way to save energy

Finnish does not need a separate word matching English to here. The infinitive form itself does that job.

Because energiaa is in the partitive case.

With säästää, Finnish often uses the partitive when talking about saving some amount of something or saving something in general:

• säästää energiaa = save energy
• säästää rahaa = save money
• säästää aikaa = save time

The idea is not usually all the energy as one complete object, but rather energy in general or an unspecified amount of energy. That is why the partitive sounds natural here.

A simple breakdown is:

• Keksimme = we came up with / we invent(ed)
• paremman tavan = a better way
• säästää energiaa = to save energy

So the structure is basically:

• verb + object + infinitive phrase

More literally, you can think of it as:

• We came up with a better way [to save energy].

The phrase säästää energiaa describes what kind of way it is.

Yes, Finnish word order is fairly flexible, because cases show what the words are doing.

The given order is a neutral, natural one:

• Keksimme paremman tavan säästää energiaa.

But other orders are possible for emphasis, for example if you want to highlight paremman tavan or place the sentence in a larger context.

Still, for a learner, the original order is the best one to treat as the default pattern.