הקרון הראשון היה מלא, ולכן עלינו לקרון השני.

In Hebrew, adjectives normally come after the noun they describe.

So:

• קרון ראשון = a first carriage
• הקרון הראשון = the first carriage

This is the standard noun + adjective order in Hebrew.

Because in Hebrew, when a noun is definite (the...), its adjective usually has to be definite too.

So:

• קרון ראשון = a first carriage
• הקרון הראשון = the first carriage

The same thing happens later with השני:

• לקרון השני = to the second carriage

This agreement in definiteness is very important in Hebrew.

קרון means a train car / carriage / railcar, not the whole train.

So:

• רכבת = train
• קרון = a carriage / car of the train

That is why the sentence talks about the first carriage and the second carriage.

Both היה and מלא match קרון, which is masculine singular.

• קרון = masculine singular noun
• היה = was (masculine singular)
• מלא = full (masculine singular)

If the noun were feminine singular, you would expect:

• הייתה מלאה

So Hebrew is showing grammatical agreement here.

ולכן means and therefore, and so, or therefore.

It is made of:

• ו־ = and
• לכן = therefore / so

It is very common in written and careful spoken Hebrew. In more casual speech, people might also use words like אז depending on the situation.

Here עלינו means we got on / we boarded / we went up into.

It is the past tense, first person plural form of the verb לעלות (to go up / to get on / to board).

So:

• עליתי = I got on / I went up
• עלינו = we got on / we went up

This verb is often used for boarding transportation.

A very important note: עלינו can also mean on us in other contexts. Hebrew spelling often allows this kind of ambiguity, and you tell the meaning from context. Here, because it is followed by לקרון השני, it is clearly the verb: we boarded / we went up to the second carriage.

Because Hebrew verbs already show the subject.

עלינו already tells you we. So אנחנו is not necessary.

Hebrew often leaves subject pronouns out when the verb already makes the person clear.

• עלינו = we got on
• אנחנו עלינו = we got on too, but with extra emphasis or contrast

So the version in the sentence is natural and normal.

Because the preposition ל־ (to) combines with the definite article ה־ (the).

So:

• ל + הקרון becomes לקרון

This is very common with the short prepositions:

• ב + ה... → ב... with the article absorbed
• כ + ה... → כ...
• ל + ה... → ל...

So לקרון means to the carriage.

Even though the ה־ disappears from the noun after ל־, the adjective still keeps its article:

• לקרון השני = to the second carriage

Because only the noun’s article gets absorbed into the preposition ל־.

So:

• לקרון = to the carriage
• השני still stays the second

That gives:

• לקרון השני = to the second carriage

This can look strange at first to English speakers, but it is completely normal Hebrew structure.

A natural pronunciation is:

ha-ka-RON ha-ri-SHON ha-YA ma-LE, ve-la-KHEN a-LI-nu la-ka-RON ha-she-NI

A few helpful notes:

• קרון = ka-RON
• ראשון = ri-SHON
• לכן has the Hebrew kh sound, like the ch in Bach
• עלינו = a-LI-nu
• שני here is she-NI

So the full sentence flows like:

ha-ka-RON ha-ri-SHON ha-YA ma-LE, ve-la-KHEN a-LI-nu la-ka-RON ha-she-NI