Sometimes languages just don't make sense, do they? Why, for instance, is "backyard" sometimes correct in English, but not always? And why is "frontyard" never correct? Let's take a look at these and similar constructions and see what conclusions we draw.
This answer's title gives a name to these two-word combinations: compounds. Sometimes they are further described as open or closed, depending on whether they are expressed as two words or one.
Another thing to note about these two-word compounds is that each of them consists of an adjective (front or back) and a noun (yard, seat, or door). There's a general rule in English that such compounds are open when they are used as nouns, but either closed or (in some cases) hyphenated when they are used as adjectives:
By the end of the morning, the four children had discovered that it was difficult to enjoy ordinary adventures when you knew that you could be having magical adventures instead.
"Good riddance!" Mrs. Beedle shouted at them, waving her broom threateningly. They fled through her backyard gate, down the street, and into their own weedy back yard.
"I don't think there was anything special about her old birdbath anyway," groused Martha, who was the hottest and the most out of breath because her legs were shortest.
"I get the front seat!" called Mark, narrowly beating Jane to Mr. Smith's car.
"That's not fair!' wailed Martha. "I get sick in the back seat."
Katherine said nothing, but her saintly expression was not lost on their stepfather.
"I think it's Katherine's turn," he said, and that was that.
The ride to town was enjoyable despite the argument at the start, except when Mark tried to persuade Mr. Smith that Gallows Road might make an interesting shortcut. "No, Uncle Huge," whimpered Martha. "That sounds much too scary!"
"Spoilsport!" Jane said, under her breath.
Perhaps she was not as quiet as she intended to be. "That's enough backseat driving, you two," said Mr. Smith. "Look, here's the drugstore. I think they may have a soda fountain." And indeed, the sign on the sidewalk outside had a beautiful ice cream soda drawn in brilliantly colored chalk.
This question of noun vs. adjective at least partially answers the question about why "backyard" is sometimes correct. But why is "frontyard" not correct?
"Because it's not" doesn't satisfy an inquiring mind, but that answer may have to do. I will note that there is a tendency for compounds that are used frequently to become closed. Those who remember the early days of the World Wide Web may remember references to "web sites," which are now almost always called "websites." The same process changed "data base" to "database." Compounds with "back-" are more common than those with "front-," and I would hypothesize that this is because "front" is the default situation when something has both a front and a back:
Martha knocked and knocked at the door of the little grey cottage, but no one answered for what seemed like hours. Finally, just as she was about to give up, a head wrapped in a spotted red kerchief poked out of the window on the left.
"Solicitors use the back door!" she snapped.
There's no need to specify that the door at which Martha is knocking is the front door: we assume that's the case when nothing further is specified.
To summarize: compounds of back plus a noun are open (two words) when used together as a noun but may be closed (one word) as an adjective. Compounds of front plus a noun are typically open (two words) in either case. But these rules aren't infallible, and a good dictionary will be your best friend if you have any doubts.