stemmen
to lift
To lift or press up something heavy with great physical effort.
Der Gewichtheber konnte die Hantel mühelos über seinen Kopf stemmen.
The weightlifter was able to lift the barbell over his head effortlessly.

to lift / brace / manage
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to lift
To lift or press up something heavy with great physical effort.
Der Gewichtheber konnte die Hantel mühelos über seinen Kopf stemmen.
The weightlifter was able to lift the barbell over his head effortlessly.

The different meanings of 'stemmen' share one idea: you apply great force or effort to overcome resistance. That can be a heavy weight, a problem, or a difficult task.
Sie musste den schweren Koffer auf das Gepäckband stemmen.
She had to lift the heavy suitcase onto the luggage belt.
In the literal meaning, 'stemmen' is always used with heavy objects. Typical objects are 'Gewichte' (weights), 'Hanteln' (dumbbells/barbells), 'Möbel' (furniture), or 'Kisten' (boxes/crates).
Zusammen haben wir das Sofa in den dritten Stock gestemmt.
Together we lifted the sofa up to the third floor.
In the meaning 'Widerstand leisten' (to resist), the verb is reflexive and is always used with the preposition 'gegen' + accusative: 'sich gegen etwas stemmen' (to brace oneself against something / to resist something).
Die Mitarbeiter stemmten sich gegen die geplanten Kürzungen.
The employees braced themselves against the planned cuts.
The meaning 'eine schwierige Aufgabe bewältigen' (to manage a difficult task) is informal. It is often used for major challenges, especially financial or organizational ones.
Als kleines Unternehmen können wir so einen großen Auftrag nicht allein stemmen.
As a small company, we can't manage such a large order on our own.
This meaning of 'stemmen' is a technical term from crafts, especially woodworking and stoneworking. You can recognize it from the context and often from the mention of the tool, the 'Stemmeisen' (chisel).
Der Tischler stemmte ein Loch für die Verbindung in das Holz.
The cabinetmaker chiseled a hole in the wood for the joint.
to manage / create
'schaffen' and 'stemmen' can both mean that you manage a difficult task. 'schaffen' is the normal and neutral word here. You use it for exams, appointments, work, or personal goals. 'stemmen' sounds more colloquial and emphasizes more strongly that something is big, difficult, or strenuous. Learners may confuse the words because both express success with a task. As a guide: you can 'eine Aufgabe schaffen' (manage a task); you can 'ein besonders großes Projekt' or 'eine große Belastung stemmen' (manage a particularly big project or a major burden).

Das kleine Team stemmt das ganze Projekt, obwohl mehrere Kollegen krank sind.
The small team is managing the whole project, even though several colleagues are sick.
Wenn ich heute früher anfange, schaffe ich die Hausaufgaben noch vor dem Training.
If I start earlier today, I will still manage to finish my homework before training.