Dopo la discussione, cerchiamo un po’ di pace in giardino.

Dopo means after.

In Italian, dopo can be used as a preposition, so it can be followed directly by a noun phrase:

• dopo la discussione = after the discussion / after the argument

You do not need another preposition between them. This works like:

• dopo pranzo = after lunch
• dopo il film = after the film

Italian uses definite articles much more often than English.

So la discussione literally means the discussion, and in many contexts English might simply say after the discussion or even just after arguing, depending on the situation.

Using the article here makes the event sound like a specific discussion already known in context.

It can mean either, depending on context.

• discussione can be a neutral discussion
• but it can also mean an argument or heated exchange

In this sentence, because it is followed by cerchiamo un po’ di pace, it strongly suggests something tense or unpleasant, so an English speaker might naturally understand it as argument.

Cerchiamo is the 1st person plural of cercare in the present indicative:

• io cerco = I look for
• tu cerchi = you look for
• noi cerchiamo = we look for

So cerchiamo means we look for, we seek, or sometimes we’re trying to find.

In this sentence, it expresses what we are doing after the discussion.

Italian often uses the simple present where English might prefer a progressive form.

So:

• cerchiamo can mean we look for
• but in context it can also mean we are looking for

Italian does have stare + gerundio:

• stiamo cercando = we are looking for

But the simple present is very natural here and does not sound incomplete to an Italian speaker.

Un po’ di means a little, a bit of, or some.

So:

• un po’ di pace = a little peace / some peace

It is a very common structure in Italian:

• un po’ di tempo = a little time
• un po’ d’acqua = a little water
• un po’ di silenzio = a little silence

The apostrophe in po’ shows that the word is shortened from poco.

So:

• un poco di pace = a little peace
• un po’ di pace = a little peace

Un po’ is much more common in everyday Italian.

After expressions of quantity, Italian normally uses di before the noun.

So:

• un po’ di pace
• molto tempo
• poco denaro
• un bicchiere d’acqua

Here di links the quantity expression un po’ to the noun pace.

Because pace is being used as an uncountable idea, not as a specific, identified thing.

So:

• un po’ di pace = a little peace / some peace

You would not normally say un po’ della pace here, because that would mean something more like a little of the peace, which sounds unnatural in this context.

Both can be possible, but they are not exactly the same.

• in giardino often means in the garden / out in the garden in a more general sense
• nel giardino means in the garden with a stronger sense of a specific, defined garden

So:

• cerchiamo un po’ di pace in giardino = we seek a bit of peace out in the garden
• cerchiamo un po’ di pace nel giardino = we seek a bit of peace in the garden

The version with in giardino sounds a little lighter and more idiomatic in many everyday contexts.

It is not strictly necessary, but it is natural.

Dopo la discussione is an introductory phrase, and Italian often uses a comma after that kind of opening element, especially in careful writing.

So both are possible:

• Dopo la discussione, cerchiamo un po’ di pace in giardino.
• Dopo la discussione cerchiamo un po’ di pace in giardino.

The comma simply marks a pause.

Yes. Italian word order is flexible, although some versions sound more natural than others.

For example:

• Dopo la discussione, cerchiamo un po’ di pace in giardino.
• In giardino, cerchiamo un po’ di pace dopo la discussione.
• Cerchiamo un po’ di pace in giardino dopo la discussione.

The original sentence is very natural because it sets the time first, then the action, then the place. That order is clear and smooth.