What is an adjective infinitive phrase?

see the explanation below.

maybe, you mean an infinitive phrase that functions as an adjective.

Let's define the concepts first.

Adjectives are words describing an idea.

Infinitive is a kind of verbal or fake verb having the formula to + base form of the verb.

Examples:to walk, to talk, to run, to plan, to encode, to watch, to dance, to play

Infinitive phrase is a phrase composed of infinitive and the words/ ideas following it.

Example:

to eat right, to solve the difficult equation, to speak in English

In the second example, to solve is the infinitive and the difficult equation is the additional idea.

When we say adjective infinitive phrase, it is an infinitive phrase that describes a noun or the idea that comes first before it.

Examples:

##1.##The instructions to follow right away is very unclear.

"to follow right away" is the adjective infinitive phrase and "the instruction" is the noun being describe.

##2.## The place to visit amazingly is Paris.

"to visit amazingly" is the adjective infinitive phrase and "the place" is the noun being describe.

Hope this helps.