The adjective capable is not followed by an infinitive (to + base verb). Instead, we use the pattern capable of doing something: ✅ She is capable of learning multiple languages simultaneously. ❌ She is capable to learn multiple languages simultaneously.

The adjective capable should be followed by the preposition of and a gerund (an “-ing verb” acting as a noun), not by an infinitive (a verb with to): capable to solve this problem capable of solving this problem

The correct phrase is 'capable of'. 'Capable of' is the standard construction used in English to indicate someone's ability or capacity to do something. 'Capable to' is not a common or correct phrase in English. This phrase is correct and commonly used in English.

It is part of the infinitive to write. MissFit explains the grammar, but the usage can also be a little different. "Able to" is the more generic and all purpose phrase and connotes ability. "Capable of" can mean that, but is frequently more indicative of propensity.