Minun on helpompi lukea sana, kun lasken tavut hitaasti.

This is a very common Finnish structure.

• Minun on helpompi lukea... literally works like For me, it is easier to read...
• Finnish often uses genitive + on + adjective + infinitive for meanings like:
  • it is easy for me to...
  • it is hard for me to...
  • it is possible for me to...

So:

• minä olen = I am
• minun on here = for me it is

That is why Minä olen helpompi would be wrong here. It would sound like I am easier, which is a completely different meaning.

Helpompi is the comparative form of helppo, which means easy.

• helppo = easy
• helpompi = easier

So the sentence uses easier, not easy.

Like in English, the comparison does not always need to be stated explicitly. Here it means something like:

• It is easier for me to read a word when...
• in other words, easier than otherwise

Finnish, like English, can use a comparative without stating the second half explicitly.

So helpompi here means:

• easier than before
• easier than when I do not count the syllables
• easier in that situation

The comparison is understood from context. This is completely normal.

Because after on helpompi, Finnish uses the infinitive to express the action.

• lukea = to read
• luen = I read / I am reading

So:

• Minun on helpompi lukea = It is easier for me to read

This is similar to English easier to read, where English also uses to read, not I read.

Here sana is the object, and its form follows Finnish object rules.

In this kind of sentence, the object can appear as a total object in the nominative singular:

• lukea sana = read the word / read a word completely

Why not the others?

• sanan would not be used here in this construction
• sanaa would be partitive and would suggest a more incomplete, ongoing, or non-total action

So sana fits the idea of successfully reading the whole word.

Also, sana here can be understood generically: not necessarily one special word, but a word / words of this kind in general.

Here kun means when.

So:

• kun lasken tavut hitaasti = when I count the syllables slowly

It introduces a subordinate clause that tells you the circumstance in which something is easier.

Important note:

• kun can sometimes have other shades of meaning in Finnish, depending on context
• but in this sentence, when is the natural meaning

Because Finnish usually leaves out the subject pronoun when the verb ending already shows the person.

• lasken already means I count
• the ending -n tells you it is I

So minä is unnecessary unless you want emphasis or contrast.

Compare:

• lasken = I count
• minä lasken = I count / I am the one counting

In neutral Finnish, leaving out minä is more natural.

Tavut is the plural form of tavu, which means syllable.

• tavu = syllable
• tavut = syllables

In the sentence, tavut is the object of lasken:

• lasken tavut = I count the syllables

This form suggests the syllables are being counted as a whole set.

If you said tavuja instead, that would be the partitive plural and would sound more like:

• syllables in general
• some syllables
• syllables as an ongoing or non-total activity

Because hitaasti is an adverb, and it modifies the verb lasken.

• hidas = slow (adjective)
• hitaasti = slowly (adverb)

Here the sentence needs an adverb, because it describes how the counting happens:

• lasken hitaasti = I count slowly

This is similar to English:

• slow = adjective
• slowly = adverb

Because Finnish normally separates a main clause and a subordinate clause with a comma.

Here:

• main clause: Minun on helpompi lukea sana
• subordinate clause: kun lasken tavut hitaasti

So the comma is standard Finnish punctuation.

If the kun clause came first, Finnish would still use a comma:

• Kun lasken tavut hitaasti, minun on helpompi lukea sana.

The given word order is natural and neutral, but Finnish word order is fairly flexible.

The sentence as written:

• Minun on helpompi lukea sana, kun lasken tavut hitaasti.

You could also say:

• Kun lasken tavut hitaasti, minun on helpompi lukea sana.

Both are correct.

The difference is mostly about emphasis:

• starting with Minun on helpompi... focuses first on the result
• starting with Kun lasken... focuses first on the condition

So the original version is not the only possible order, but it is a very normal one.

Yes, roughly like this:

• Minun = for me / my
• on = is
• helpompi = easier
• lukea = to read
• sana = word
• kun = when
• lasken = I count
• tavut = syllables
• hitaasti = slowly

A very literal version would be:

• For me is easier to read a word, when I count the syllables slowly.

That is not natural English, but it helps show how Finnish builds the sentence.