Kibao kilicho mbele ya ofisi kinaonyesha njia ya kwenda maktaba.

Because both words are agreeing with kibao, which belongs to noun class 7 in Swahili.

• kibao = class 7 singular
• its plural would be vibao = class 8 plural

Swahili often makes verbs and modifiers agree with the noun class of the noun they describe. So:

• ki- matches kibao
• if it were plural vibao, you would expect vi- forms instead

kilicho means which is or that is, agreeing with kibao.

So:

• kibao kilicho mbele ya ofisi = the sign that is in front of the office

It is a relative form, used to connect kibao with the description that follows it.

mbele ya means in front of.

Literally:

• mbele = front
• ya = of
• mbele ya ofisi = the front of the office, i.e. in front of the office

This is a very common Swahili pattern:

• nyuma ya nyumba = behind the house
• karibu na shule = near the school

Because mbele ya already gives the location relationship: in front of. After expressions like mbele ya, the following noun is usually just the plain noun:

• mbele ya ofisi = in front of the office

Using ofisini would add a locative idea to ofisi itself, but here the location is already clearly expressed by mbele ya.

kinaonyesha comes from the verb -onyesha, meaning to show.

It breaks down like this:

• ki- = subject marker agreeing with kibao
• -na- = present tense
• -onyesha = show

So kinaonyesha means it shows or it is showing.

Swahili does not normally use articles like English a or the.

So a noun like kibao can mean:

• a sign
• the sign

The exact meaning comes from context. In this sentence, English naturally uses the sign.

Literally, it means the way of going to the library.

More naturally in English:

• the way to the library
• the direction to the library

Breakdown:

• njia = way, path, route, direction
• ya = of
• kwenda maktaba = going to the library

The ya is a connector meaning something like of. It agrees with njia, which is in noun class 9.

So:

• njia ya kwenda = way of going
• more naturally: way to go / route for going

This kind of linker is very common in Swahili:

• kitabu cha mwanafunzi = the student's book
• chakula cha asubuhi = breakfast
• njia ya kwenda mjini = the way to town

After kwenda (to go), Swahili can express the destination without adding a separate word that matches English to exactly.

So:

• kwenda maktaba = go to the library

You may also hear other natural alternatives such as:

• kwenda maktabani
• kwenda kwenye maktaba

All of these can express the idea of going to the library, though the exact style may vary by context and speaker.

Yes. That would also be correct and would mean essentially the same thing:

• kibao ambacho kiko mbele ya ofisi

This version is a bit more explicit:

• ambacho = which/that
• kiko = it is located

The original kibao kilicho mbele ya ofisi is a more compact way to say the sign that is in front of the office.

It can be divided into three main parts:

1. Kibao kilicho mbele ya ofisi
   = The sign that is in front of the office

2. kinaonyesha
   = shows

3. njia ya kwenda maktaba
   = the way to the library

So the sentence structure is:

[subject noun phrase] + [verb] + [object phrase]

That is very normal word order in Swahili.