This question tests your understanding of gerunds and verb forms in sentence structure. Let's break it down step-by-step.

Step 1: Analyze the first blank.

The first blank is at the beginning of the sentence, before the noun phrase "a foreign language". This position is often filled by a verb form that acts as a noun, which is called a gerund. A gerund is a verb ending in "-ing" that functions as a subject or an object. The subject of this sentence is the act of "knowing a foreign language". Therefore, the correct form for the first blank is knowing.

Using "knows" (a finite verb) here would be grammatically incorrect because it cannot act as the subject of the sentence.

Step 2: Analyze the second blank.

The second blank comes after the modal verb "can". A fundamental rule of grammar is that modal verbs (like can, could, will, would, shall, should, may, might) are always followed by the base form (also called the bare infinitive) of the main verb. The base form is the simplest form of the verb, without "to".

Therefore, after "can", we must use have, not "having" (a gerund) or "to have" (a to-infinitive).

Step 3: Final Answer.

The completed sentence is: Knowing a foreign language you can have great opportunities in life.

"Knowing" acts as the gerund subject, and "have" is the base form of the verb that correctly follows the modal verb "can".

Related Concepts & Formulae

Gerunds: A gerund is a verb form that ends in "-ing" and functions as a noun. It can be the subject or object of a sentence.

Formula: $Verb+ing=Gerund(Noun)$

Example: Swimming is good exercise. (Swimming is the subject).

Modal Verbs: Modal verbs express ability, possibility, permission, or obligation. They are always followed by the base form of the main verb.

Formula: $Modal Verb+Base Form$

Examples: She can speak French. You should study more.