This is the 2235th most frequent Turkish word.
almasına
"Almasına" means "for him/her/it to take/receive" or "taking/receiving."
In this sentence, 'bırakmasına' is derived from the verb 'bırakmak' meaning 'to leave' or 'to drop'. The suffix '-masına' implies an action in its noun form, often translated as 'to...' or 'for...' in English. Here, it refers to the action of 'dropping' (of school).
Onun okulu bırakmasına kadar birçok neden vardı.
There were many reasons for him dropping out of school.
'Yağmasına' comes from the verb 'yağmak,' meaning 'to rain'. The construction adds a sense similar to 'for raining' or 'that it rained'. It expresses the event of the rain in a nominalized form.
Yağmurun erken yağmasına sevindim.
I was glad for the rain coming early.
'Almasına' in this context stems from 'almak', meaning 'to take' or 'to receive'. The structure gives a sense related to the act of 'taking' as an occurrence influenced in the sentence.