My pleasure. I may have shared this here before; I can't remember.
COMPOUND ADJECTIVES
A compound adjective is formed when two (or more) words are used together to describe or modify a noun. They are hyphenated when they come before the noun, but not if they come after it unless needed for clarity.
TEMPORARY COMPOUND ADJECTIVES
A temporary compound adjective is formed when the two words together assume a different meaning than their separate meanings. Writers who form temporary compounds should generally hyphenate them when they are used as adjectives and appear before the noun. If the compound adjective appears after the noun, hyphenate only if it’s needed for clarity.
Examples of compound adjectives (all hyphenated because they are both temporary and come before the noun): hard-nosed boss, ill-fated voyage, mass-produced shoes, whacked-out psycho, thrown-together salad, up-to-the-minute news.
TO TEST...
Have you created a compound adjective, or just put two descriptive words together? To check, see if you can remove either word without making nonsense or changing the meaning of the remaining word. A tall frosty glass of beer still makes sense if either ‘tall’ or ‘frosty’ is removed, so it is not a compound. However, blue-ribbon pie requires both ‘blue’ and ‘ribbon’ and should therefore be hyphenated before the word ‘pie.’
Second example: Boston is about to elect its first non-white-male mayor versus Boston is about to elect its first non-white male mayor.
NOTE:
Some compound adjectives change meaning, depending on whether they're hyphenated: a fast-sailing ship/a fast sailing ship, or free-form sculpture/free form sculpture. A long-gone crazy weatherman is not the same as a long-gone-crazy weatherman. A black-robed judge is not a black robed judge, nor is a gay-rights activist a gay rights activist.
TEMPORARY COMPOUND NOUNS
A compound noun is formed when two (or more) words are used together to form a single concept. Such a combination is far more unusual than a compound adjective.
Generally when they’re created they tend to start as two words, become hyphenated as use becomes widespread, then finally joined into a single word by the time use is common, if indeed that happens.
Examples of compound nouns include tomorrow, motherf***er, speedboat, and textbook.
PERMANENT COMPOUNDS
When the compound is accepted into the general vocabulary of English and can (or should) be found in dictionaries, the trend in spelling has been away from hyphenating and toward spelling them "solid" or "closed" (i.e., as a single word). Examples of closed compound nouns: notebook, motorcycle, email, and bedroom. Examples of closed compound adjectives: underrated, halfhearted, midlife, and childproof.
Open compounds are combinations of words which constitute a single concept but are still spelled as separate words, often without a hyphen. Usually the only reason is that the words don't join well. Examples of open compounds are: stool pigeon, gun shot wound, and high school.
There are special rules for compounds using the words half, like, time, and adverbs ending in -ly, as well as special rules for colors. When in doubt, check the online version of Merriam Webster for current practices or their print dictionary if it's less than two years old.