right away vs forthwith

right away and forthwith both are adverbs.

Word	Noun	Adjective	Verb	Adverb
right away	No	No	No	Yes
forthwith	No	No	No	Yes

As adverbs, right away and forthwith are synonyms defined as:

right away and forthwith: without delay or hesitation; with no time intervening

Other synonyms of right away include at once, directly, immediately, instantly, like a shot, now, straight off, straightaway.

right away (adverb)	forthwith (adverb)
without delay or hesitation; with no time intervening	without delay or hesitation; with no time intervening
at once (usually modifies an undesirable occurrence)