على الرغم من المطر، يحمل أبي صندوق الأدوات إلى البيت.

Yes. على الرغم من is a very common fixed expression meaning despite, in spite of, or although there is.

In this sentence:

• على الرغم من المطر = despite the rain / in spite of the rain

You do not usually translate it word for word. It is best learned as one chunk.

A literal breakdown is roughly:

• على = on/upon
• الرغم = unwillingness / despite
• من = of / from

But for learners, the important thing is:

• على الرغم من + noun
• على الرغم من + verbal noun / clause

So here, على الرغم من المطر simply means despite the rain.

Because على الرغم normally takes من after it.

So the pattern is:

• على الرغم من + noun

Examples:

• على الرغم من المطر = despite the rain
• على الرغم من التعب = despite the tiredness
• على الرغم من الصعوبات = despite the difficulties

So من is not optional here in standard usage. It is part of the expression.

In normal Arabic writing, short case endings are usually not written.

After the preposition من, the noun should be in the genitive case, so fully vowelled it would be:

• المطرِ

But in ordinary text, Arabic usually leaves off the final short vowel, so you see:

• المطر

The same thing happens all through this sentence: the grammatical case is there, but the short vowel is just not written.

يحمل is the imperfect form of the verb حمل.

Depending on context, the Arabic imperfect can mean:

• carries
• is carrying
• does carry
• sometimes even will carry

In this sentence, the most natural English is probably:

• My father carries the toolbox home despite the rain or
• My father is carrying the toolbox home despite the rain

So يحمل is present/imperfect, and English chooses the best translation from context.

Because Arabic often uses verb-subject-object order, especially in more formal styles like Modern Standard Arabic.

So:

• يحمل أبي صندوق الأدوات = literally carries my father the toolbox

This is perfectly normal Arabic word order.

You could also say:

• أبي يحمل صندوق الأدوات

That is also correct, but it puts a little more emphasis on أبي as the topic: My father is carrying the toolbox.

So:

• يحمل أبي... = standard VSO order
• أبي يحمل... = also correct, slightly different focus

Because أبي is made of:

• أب = father
• ـي = my

So:

• أبي = my father

This suffix ـي is very common:

• بيتي = my house
• كتابي = my book
• اسمي = my name

So in the sentence:

• يحمل أبي = my father carries / my father is carrying

This is because أب belongs to a special group often called the five nouns in Arabic grammar.

Normally, these nouns show case with long vowels in certain constructions, but when أب is attached to the first-person singular suffix ـي (my), the form is commonly written as:

• أبي

So although أبي is the subject here, it still appears as أبي in normal spelling.

In other words:

• جاء أبي = my father came
• رأيت أبي = I saw my father
• مررت بأبي = I passed by my father

In fully formal grammatical analysis, the case is still different by function, but the written form with ـي stays أبي.

For a learner, the key point is simple:

• أبي = my father

This is an iḍāfa construction, often called a genitive construction or noun + noun construction.

It is:

• صندوق = box
• الأدوات = the tools

Together:

• صندوق الأدوات = toolbox
• more literally: box of the tools

Arabic often expresses this kind of idea with two nouns placed together instead of using of.

Other examples:

• باب البيت = the door of the house
• كتاب الطالب = the student’s book
• غرفة النوم = bedroom, literally room of sleeping

So صندوق الأدوات is the natural Arabic way to say toolbox.

In an iḍāfa construction, if the second noun is definite, then the whole phrase is definite.

Here:

• الأدوات has الـ, so it is definite: the tools
• therefore صندوق الأدوات is also definite

So grammatically, this phrase is:

• the toolbox

not just a toolbox

This is an important rule:

• كتاب طالب = a student’s book / a book of a student
• كتاب الطالب = the student’s book

So in your sentence, صندوق الأدوات is definite because الأدوات is definite.

It is the direct object of the verb يحمل.

So the structure is:

• يحمل = carries
• أبي = my father
• صندوق الأدوات = the toolbox

That means:

• my father carries the toolbox

If the text were fully vowelled, صندوق would be in the accusative case because it is the direct object:

• صندوقَ الأدواتِ

But again, normal Arabic writing usually leaves those short vowels unwritten.

إلى means to / toward, so:

• إلى البيت = to the house / home

A few points:

1. إلى is the normal preposition for movement toward a destination.
2. البيت is definite here: the house.
3. In many contexts, Arabic uses the house where English would simply say home.

So:

• إلى البيت can often be translated naturally as home

Using إلى بيت would mean to a house, which is less specific.

Using لـ would usually express something different, such as for the house or belonging to the house, not simple movement toward it.

If we fully vowel the sentence, it would look like this:

• على الرغمِ من المطرِ، يحملُ أبي صندوقَ الأدواتِ إلى البيتِ.

Here is the grammar:

• على الرغمِ: الرغمِ is after a preposition, so it is genitive
• من المطرِ: المطرِ is genitive after من
• يحملُ: verb
• أبي: subject in the nominative by function
• صندوقَ: direct object, so accusative
• الأدواتِ: second term of iḍāfa, so genitive
• إلى البيتِ: البيتِ is genitive after إلى

This is a very good example of how Arabic grammar is present even when the short vowels are not written.

A careful pronunciation would be approximately:

• ʿalā r-raġmi mina l-maṭari, yaḥmilu abī ṣundūqa l-adawāti ilā l-bayti.

A simpler learner-friendly transliteration:

• ala r-raghmi min al-matar, yahmilu abi sunduq al-adawat ila al-bayt

A few pronunciation notes:

• ع in على is a deep throat sound with no exact English equivalent.
• غ in الرغم is like a French-style r or a throaty sound.
• ح in يحمل is a stronger, breathier h than English h.
• ط in المطر is an emphatic t.
• ص in صندوق is an emphatic s.

If you want to sound natural, try saying it in chunks:

• على الرغم من المطر
• يحمل أبي
• صندوق الأدوات
• إلى البيت

That makes the rhythm much easier.