A "compound adjective" is a descriptive phrase that consists of multiple words. Hyphens are used to group words together so it's clear how the words relate to each other. Multiple hyphens may be necessary.
The maps show the distribution of H2S bearing hydrocarbons. [The H2S bears hydrocarbons?]
vs. The maps show the distribution of H2S-bearing hydrocarbons. [It's clear the hydrocarbons bear H2S]
It's a natural-gas-fired plant; The plant is natural-gas fired; The plant is fired by natural gas.
In general, compound adjectives are hyphenated when they appear before the noun they modify, but they are not hyphenated when they appear after the noun.
ill-advised choice; well-intentioned person
BUT: The choice was ill advised, the person well intentioned.
When a word is common to two or more compound adjectives in a series, it may be replaced by a hyphen followed by a space, except for the final occurrence:
You can choose to take a one- or two-week course.
You can choose to take a one-, two-, or three-week course.
Never use a hyphen after adverbs ending in ly.
a highly regarded scientist
a well-thought-of scientist
Hyphenate two equal nouns used as a single noun:
student-teacher relationship
Compounds including a verb (like coal mining, decision making, and problem solving) follow the same rules as above: hyphenate when they appear as adjectives before the noun, do not hyphenate otherwise.
coal-mining activity; decision-making authority
The AER regulates coal mining; The manual guides decision making.