Learn Spanish (Latin America): El carro de mi hijo es azul, pero el de mi esposo es negro. - My son's car is blue, but my husband's is black.

el de acts like a shortcut. Instead of repeating the noun and saying el carro de mi esposo (my husband's car), we drop the word carro and just say el de (the one of). We use el because carro is a masculine, singular noun.

Why does the sentence use El carro de mi hijo instead of something with an apostrophe like "Mi hijo's carro"?

Spanish does not use an apostrophe "s" to show ownership. To say "my son's car", you always have to rephrase it as "the car of my son" which is exactly what El carro de mi hijo means.

If we were talking about bicycles (bicicletas) instead of cars, how would the shortcut change?

Because bicicleta is a feminine noun, you would use la instead of el. The second half of the sentence would become pero la de mi esposo es negra. Notice that the adjective negra also changes to feminine to match the hidden bicycle!

Why does the adjective negro match the car when it is sitting right next to the word esposo (husband)?