Wavu wa goli umeharibika, kwa hiyo kocha anatafuta mwingine.

Because the linker has to agree with wavu, not with goli.
Wavu belongs to a noun class that uses wa as the associative linker, so wavu wa goli is correct.

If the first noun belonged to a different class, you might get ya, la, cha, and so on.

It breaks down like this:

• u- = subject prefix agreeing with wavu
• -me- = perfect marker
• haribika = be damaged / get spoiled / become broken

So umeharibika means something like has become damaged or is damaged.

A useful contrast is:

• kuharibu = to damage something
• kuharibika = to be damaged / to get damaged

So this sentence uses the intransitive form, because the net itself is in a damaged state.

Because the verb has to agree with the noun wavu.
Swahili verbs use different subject prefixes for different noun classes, not just for person.

Here, wavu takes the subject prefix u-, so:

• wavu umeharibika = the net is damaged

If the noun were from a different class, the prefix would change.

It is the perfect form, marked by -me-. In English, that often comes out as:

• has become damaged
• has gotten damaged
• or simply is damaged, if the result is what matters

So it is not a simple one-to-one match with English tense. The idea is that the damage has already happened and the result is true now.

Kwa hiyo means so, therefore, or for that reason.
It connects the first idea to the second:

• the goal net is damaged
• so / therefore the coach is looking for another one

It is a very common way to show consequence.

Because anatafuta contains:

• a- = he/she
• -na- = present tense marker
• tafuta = look for / search for

So anatafuta can mean:

• he/she is looking for
• he/she looks for

In this sentence, English naturally uses the progressive: the coach is looking for another one.

Here mwingine means another one or a different one.
The noun itself is left out because it is understood from context.

So:

• kocha anatafuta mwingine = the coach is looking for another one

The understood noun is wavu. In fuller form, you could say:

• kocha anatafuta wavu mwingine = the coach is looking for another net

By form alone, mwingine can sometimes be ambiguous, because it can match more than one noun class. So if you only looked at that one word, you might wonder what it refers to.

But in this sentence, context makes it clear that it means another net, not another coach. The first clause talks about the net being damaged, so that is the thing the coach is trying to replace.

If you want to remove any possible ambiguity, you can say:

• kocha anatafuta wavu mwingine

Because Swahili does not normally use articles like a, an, and the.
Whether a noun is definite or indefinite is usually understood from context.

So wavu wa goli could mean:

• a goal net
• the goal net

And kocha could mean:

• a coach
• the coach

In this sentence, context makes the goal net and the coach sound most natural in English.

They are common loanwords, especially in sports language.

• goli comes from English goal
• kocha comes from English coach

Even though they are loanwords, they still behave like Swahili words in the sentence and fit into Swahili grammar normally.