Tele van a piknikkosár, úgyhogy külön visszük a termoszt.

Tele means full, but in Hungarian the common predicate is the expression tele van, literally something like is full.

So:

• Tele van a piknikkosár. = The picnic basket is full.

This is a very normal Hungarian structure. You should learn tele van as a set phrase.

You can also say what something is full of:

• A kosár tele van étellel. = The basket is full of food.

In your sentence, the content is not named; it just says the basket is full.

Both are possible, but the word order changes the focus slightly.

• Tele van a piknikkosár. puts emphasis on the state full.
• A piknikkosár tele van. is also correct and feels more like The picnic basket is full with the basket as the starting topic.

Hungarian word order is flexible and often reflects emphasis and information structure rather than strict English-style sentence order. In this sentence, starting with tele highlights the reason for what comes next.

Úgyhogy means so, therefore, which is why, or that’s why.

In this sentence:

• Tele van a piknikkosár, úgyhogy külön visszük a termoszt.
• The picnic basket is full, so we’re carrying the thermos separately.

It is a very common connector in everyday Hungarian.

Here külön means separately or on its own.

So:

• külön visszük a termoszt = we carry the thermos separately

Be aware that külön can also mean separate, distinct, or sometimes special, depending on context. But here the adverb meaning separately is the right one.

This is because Hungarian verbs have two main conjugations:

• indefinite conjugation: used when there is no definite direct object
• definite conjugation: used when there is a definite direct object

Here the object is:

• a termoszt = the thermos

That is definite, so Hungarian uses the definite form:

• visszük = we carry it / we are carrying the specific thing

Compare:

• Viszünk egy termoszt. = We’re carrying a thermos.
  (indefinite object)
• Visszük a termoszt. = We’re carrying the thermos.
  (definite object)

Because -t is the accusative ending, which marks the direct object.

• termosz = thermos
• termoszt = thermos as the object of the verb

In this sentence, the thermos is what we carry, so it takes the accusative:

• visszük a termoszt

Hungarian often marks direct objects explicitly with -t.

Hungarian usually does not need subject pronouns when the verb ending already shows the subject.

• visszük already means we carry / we are carrying it

So adding mi (we) is usually unnecessary unless you want special emphasis:

• Mi visszük a termoszt. = We’re the ones carrying the thermos.

In normal speech, just visszük is enough.

A is the Hungarian definite article, meaning the.

So:

• a piknikkosár = the picnic basket
• a termoszt = the thermos

Hungarian uses the definite article when the speaker and listener are talking about specific, identifiable things, just like English uses the.

Hungarian very often forms compound nouns by writing them as one word.

• piknik = picnic
• kosár = basket
• piknikkosár = picnic basket

This is very normal in Hungarian. English often writes such combinations as two words, but Hungarian commonly joins them into one compound.

Visz has a broader meaning than just carry. Depending on context, it can mean:

• carry
• take
• bring away
• transport

So külön visszük a termoszt could be understood as:

• we’re carrying the thermos separately
• we’re taking the thermos separately

The exact English choice depends on context, but the Hungarian verb is very natural here.

Yes, absolutely. Hungarian word order is flexible.

These are all possible, with slightly different emphasis:

• úgyhogy külön visszük a termoszt
• úgyhogy a termoszt külön visszük

The version in your sentence puts külön in a prominent position, which highlights the idea of separately. That makes good sense, because it explains the practical consequence of the basket being full.

A rough pronunciation is:

• úgyhogy ≈ oo-y-hoj

A bit more carefully:

• ú is a long oo
• gy is a soft consonant, somewhat like the d in British duke or the gy sound learners often hear in Hungarian words like magyar
• hogy sounds roughly like hodj, but with a softer Hungarian gy

You do not need a perfect English equivalent, because the gy sound is specifically Hungarian, but the important thing is to recognize úgyhogy as one very common linking word.