mehrjährig
multi-year
Extending over a period of several years or lasting several years.
Nach seiner mehrjährigen Weltreise kehrte er endlich nach Hause zurück.
After his multi-year trip around the world, he finally returned home.

multi-year / perennial
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multi-year
Extending over a period of several years or lasting several years.
Nach seiner mehrjährigen Weltreise kehrte er endlich nach Hause zurück.
After his multi-year trip around the world, he finally returned home.

The adjective is clearly built from 'mehr' (more/several) and 'jährig', a form of 'das Jahr' (the year). It literally means 'concerning several years' or 'lasting over several years'.
Für diesen Job ist mehrjährige Berufserfahrung erforderlich.
Several years of professional experience are required for this job.
In its general meaning, 'mehrjährig' (multi-year) is often used to describe the duration of experience, contracts, or training programs. Typical phrases are 'mehrjährige Erfahrung' (several years of experience), 'ein mehrjähriger Vertrag' (a multi-year contract), or 'eine mehrjährige Ausbildung' (a multi-year training program).
Sie hat einen mehrjährigen Mietvertrag für ihre Wohnung unterschrieben.
She signed a multi-year lease for her apartment.
You can recognize the botanical meaning from words related to gardens and plants. When the topic is 'Pflanzen' (plants), 'Stauden' (perennials), or 'Kräuter' (herbs), 'mehrjährig' (perennial) means that they do not die in winter and grow again the next year.
Rosen sind mehrjährige Pflanzen, die bei guter Pflege viele Jahre blühen.
Roses are perennial plants that bloom for many years with good care.
long-term
'langfristig' and 'mehrjährig' both describe something that does not last only a short time. 'langfristig' is more general and emphasizes planning or effects over a longer time in the future. How many years are meant often remains open. 'mehrjährig' is more specific: it means that something lasts several years or extends over several years. Learners may confuse the words because both sound like a long duration. If you are talking about goals, strategies, or consequences, 'langfristig' usually fits. If the duration really is several years, 'mehrjährig' is more precise.

Für das Projekt gibt es einen mehrjährigen Plan mit festen Etappen.
There is a multi-year plan for the project with fixed stages.
Wir wollen langfristig weniger Geld für Miete ausgeben.
In the long term, we want to spend less money on rent.