Fill in the blank with a suitable homophone: They went for a ......

Because the sentence uses “a” before the blank, we need a word that can act as a noun.

The best fit is “show”, which as a noun means a performance or event you can go to watch: “They went for a show.”

• “Sow” is usually used as a verb meaning to plant seeds; as a noun it means a female pig, which doesn’t fit here.

• “Sew” is a verb meaning to stitch fabric, so it doesn’t work as something you “went for a …”.

• “Shove” means to push roughly, which doesn’t match the context.