Learn Danish: Hun har brug for en bærbar lampe af metal.

The suffix -bar works just like "-able" in English to show that something is capable of being done. Here, it is added to the root of the verb at bære (to carry). Together, they form bærbar, meaning "carry-able" or "portable".

Why does the sentence use har brug for instead of a single verb for "needs"?

While Danish does have the verb at behøve (to need), it is much more common and natural to use the fixed phrase at have brug for in everyday speech. It literally translates to "to have use for".

If lampe was a neuter word (an et word), would bærbar change?

Yes, adjectives ending in -bar follow normal adjective rules. If you were talking about a portable television (et fjernsyn), you would add a -t to match the neuter gender, making it et bærbart fjernsyn.

Could you say metallampe instead of lampe af metal?

Yes, you can form a compound noun like metallampe. However, using af (of) is a very common and flexible way to describe what material an object is made out of, just like saying "a lamp of metal" in English.