Combine sentences by using an infinitive.
I have engaged a private tutor. He will teach me English.
(a) I have engaged a private tutor so that he can teach me English.
(b) I have engaged a private tutor to teach me English.
(c) No change
(d) I have engaged a private tutor to help me teaching English.

Hint: Read the sentence and try to guess what it is trying to convey. Now go through the given options and choose the one which helps in expressing the context of the given question without changing the meaning of the sentence.

Complete answer:
Infinitives refer to those verbs that are preceded by ‘to’. For example- to run, to laugh, etc.
Let’s look at the usage of infinitives-
For example- They had to catch the train. Here, ‘to catch’ is an infinitive.
In the given question- We can conclude that X has engaged a private tutor to teach him English.
Now, let’s examine the given options-
(a) ‘I have engaged a private tutor so that he can teach me English’ is an incorrect option because we cannot see the use of a ‘to-infinitive’ in the sentence.
(b) ‘I have engaged a private tutor to teach me English’ is the correct option because we can see the use of a ‘to-infinitive’ without an alteration in the meaning of the sentence.
(c) ‘No change’ is an incorrect option because the sentence requires change.
(d) ‘I have engaged a private tutor to help me teaching English’ is an incorrect option because the to-infinitive is always used with the base form of the verb. Hence, the correct answer is Option ‘b’.

Note:
Keep in mind, we always use the first form of the verb with to-infinitives. Also, the infinitives that function without the use of ‘to’ are known as ‘bare infinitives’.