adjectival phrase

"Tobacco" is a noun, and "smoking" is a gerund.

Thus, "tobacco smoking" is not an adjectival phrase. It is a noun phrase. A noun phrase has a noun as its head, (e.g. "tobacco") and an optional modifier or set of modifiers (e.g. a verb object which might be a gerund such as "smoking")

An adjectival phrase is a phrase with an adjective as its head, for example "full of toys". Adjectival phrases may occur as postmodifiers to a noun (a bin full of toys), or as predicatives (predicate adjectives) to a verb (the bin is full of toys).

An adjective acts as the head of an adjective phrase (or adjectival phrase). In the simplest case, an adjective phrase consists solely of the adjective; more complex adjective phrases may contain one or more adverbs modifying the adjective ("very strong"), or one or more complements ("worth several dollars", "full of toys", "eager to please). In English, attributive adjective phrases that include complements typically follow their subjects ("an evildoer devoid of redeeming qualities").

Many thanks, Contrex, for your detailed reply.

I would like to say I appreciate your help very much.

Best wishes.

Yoong Liat, thank you very much for your kind remarks. Best wishes also.

However "tobacco smoking" can function as an adjective (though I'd probably use a hyphen),, OR as a noun, depending on context.

"Tobacco smoking is bad for your health" is a noun phrase as the subject.

"That tobacco-smoking son of a b*tch stinks up any room he enters"--functions as an adjective, tho maybe not an adjective phrase

A very good point, username, which illustrates the crucial importance of context.