Parvenir vs. réussir vs. arriver vs. se débrouiller

The French language has various ways to express the concept of managing to do something, with subtle differences in meaning and usage. 'Parvenir', 'réussir', 'arriver', and 'se débrouiller' are four verbs that can convey this idea, each with its own connotations and appropriate contexts.

Parvenir

It usually implies successfully reaching a goal, often after some effort or overcoming difficulties.
Il a finalement pu parvenir à ses fins malgré les obstacles.
(He finally managed to achieve his goals despite the obstacles.)
Après des années de recherche, nous sommes parvenus à une découverte majeure.
(After years of research, we have managed to make a major discovery.)

Réussir

This verb suggests success in achieving something or doing well in a particular task or area. It's similar to the English verb 'to succeed'.
Elle a réussi son examen avec brio.
(She managed to pass her exam with flying colors.)
Ils ont réussi à convaincre le jury de leur projet.
(They managed to convince the jury of their project.)

Arriver

Commonly used to mean 'to arrive', it can also mean 'to manage', especially when discussing the completion of more mundane or everyday tasks, rather than grand achievements.
Je suis arrivé à réparer la chaise tout seul.
(I managed to fix the chair by myself.)
Tu penses que tu arriveras à finir ton travail avant ce soir ?
(Do you think you will manage to finish your work before tonight?)

Se débrouiller

Implies being resourceful and managing to cope or get by, often in challenging situations or without much help. It's a bit more informal compared to the other verbs.
Malgré la difficulté de la langue, il s'est bien débrouillé pendant son séjour à l'étranger.
(Despite the difficulty of the language, he managed quite well during his stay abroad.)
Elle se débrouille toujours pour trouver des solutions créatives aux problèmes.
(She always manages to find creative solutions to problems.)

Summary

In summary, while all four French verbs can be used to convey the idea of managing to do something, 'parvenir' implies a successful outcome usually after effort; 'réussir' refers more to achieving success or doing well; 'arriver' is used for completing tasks and is more everyday; and 'se débrouiller' suggests being resourceful and coping in challenging situations. The choice between these verbs depends on context and the nuance a speaker wishes to convey.