Learn Finnish: Annan housut räätälille paikattavaksi, ja hän ompelee napin. - I give the trousers to the tailor to be patched, and he sews the button.

It uses the passive present participle ending -tava (or -ttava depending on the verb), which implies 'something that is to be done'. To this, we add the translative case ending -ksi. In Finnish, the translative case is heavily used to show purpose or an intended future state. Combined, paikattavaksi literally means 'for the purpose of being patched'.

Why is paikattavaksi in the singular form when the trousers (housut) are plural?

When the passive present participle in the translative case is used to express the purpose of an action, it acts almost like a verbal noun and usually stays in the singular (-tavaksi) regardless of whether the object is singular or plural. While the plural paikattaviksi is grammatically possible, the singular is much more common and perfectly idiomatic here.

Why does the object napin have an -n ending while housut ends in -t?

Both are total objects in the accusative case, but their endings differ because of their grammatical number. Nappi (button) is singular, so its standard accusative form looks like the genitive, taking an -n. Housut (trousers) is a plural word, and the plural accusative always looks identical to the plural nominative, ending in -t.

How do we form the passive participle paikattava from the dictionary verb ?