הוא יצא מהבית בלי העיפרון שלו, ולכן קנה עיפרון חדש בחנות.

Both are good translations here.

יצא literally means went out / exited, and in many contexts English naturally translates it as left. In this sentence, יצא מהבית is very natural Hebrew for he left the house / he went out of the house.

A useful contrast:

• יצא מהבית = he went out of the house / left home
• הלך = he went / walked

So יצא focuses on the fact that he exited a place.

In Hebrew, past-tense verbs change form according to person, number, and gender.

Here:

• יצא = he went out / he left
• קנה = he bought

These are both 3rd person masculine singular past forms, which match הוא.

So even if הוא were omitted at the start, the verb form itself would still tell you the subject is he.

Because the preposition מ־ (from) attaches directly to the noun, and when it combines with the definite article ה־ (the), the forms merge.

So:

• בית = house
• הבית = the house
• מבית = from a house / from a house-related source, depending on context
• מהבית = from the house / from home

In this sentence, מהבית means from the house or more naturally from home.

Because העיפרון שלו means his pencil, referring to a specific pencil that belongs to him.

In modern Hebrew, when you use a noun + שלו / שלה / שלהם to talk about a specific possessed thing, the noun is very often definite:

• הספר שלי = my book
• המכונית שלה = her car
• העיפרון שלו = his pencil

If you say עיפרון שלו, it can sound more like a pencil of his or one of his pencils, or just more colloquial depending on context.

So here העיפרון שלו is the normal choice for his pencil.

שלו means his or literally of him.

It comes after the noun:

• העיפרון שלו = his pencil
• הבית שלו = his house

This is different from English, where his comes before the noun.

Also, שלו agrees with the owner, not with the thing owned:

• שלו = his
• שלה = hers
• שלהם = their

So even if the noun changes, שלו stays the same as long as the owner is he.

Because את is used for a definite direct object of a verb, but העיפרון שלו here is not a direct object of a verb. It is the object of the preposition בלי (without).

So Hebrew says:

• בלי העיפרון שלו = without his pencil

not:

• בלי את העיפרון שלו ✗

After prepositions like ב, ל, מ, עם, בלי, you do not use את.

Because עיפרון חדש is indefinite: a new pencil, not the new pencil.

Hebrew uses את only before a definite direct object.

Compare:

• קנה עיפרון חדש = he bought a new pencil
• קנה את העיפרון החדש = he bought the new pencil

So in your sentence, no את is needed.

ולכן means and therefore, so, or and so.

It is built from:

• ו־ = and
• לכן = therefore / therefore so

So:

• ..., ולכן קנה... = ..., and therefore he bought...
  or more natural English: ..., so he bought...

Hebrew often uses ו very freely to connect clauses, sometimes where English might just use so or nothing at all.

Because Hebrew often omits a repeated subject when it is already clear.

The sentence starts with הוא יצא..., so once the subject has been established, Hebrew can continue with just the verb:

• הוא יצא מהבית..., ולכן קנה...

This is like English:

• He left home without his pencil, so bought a new one

That exact wording sounds incomplete in normal English, but in Hebrew it is perfectly natural because the verb form קנה already tells you he bought.

You could say ולכן הוא קנה..., but הוא is not necessary.

Because in Hebrew, adjectives normally come after the noun.

So:

• עיפרון חדש = a new pencil
• בית גדול = a big house
• חנות קטנה = a small store

Also, the adjective agrees with the noun in gender, number, and definiteness:

• עיפרון חדש = a new pencil
• העיפרון החדש = the new pencil

That is why both words would become definite together if needed.

The preposition ב־ (in / at) attaches directly to the noun, so it is written as one word:

• בחנות

A helpful thing to know is that in unpointed Hebrew writing, בחנות can represent either:

• be-chanut = in a shop / in a store
• ba-chanut = in the shop / in the store

So the exact meaning depends on context or vowel marks.

If the meaning shown to you was in the store, then you should understand this as ba-chanut. If the meaning was in a store, then it is be-chanut.

Because that is a very normal Hebrew word order.

In קנה עיפרון חדש בחנות, the order is:

• verb: קנה
• object: עיפרון חדש
• place: בחנות

This is a neutral, natural order: he bought a new pencil in the store.

Hebrew word order is somewhat flexible, so you could move בחנות earlier for emphasis, but the version in your sentence is the most straightforward.