I am unable to find the solution. A friend asked me this question What will be the passive of the sentence? "Dogs like to chase Cats"
Your friend's question implies a mistaken assumption that every active sentence can be passivized. But this assumption is generally true only for constructions with transitive verbs (i.e., verbs that can be followed by a direct object).
In the sentence Dogs like cats the verb like is transitive and followed by the direct object cats. Hence it can be passivized:
Cats are liked by dogs.
But in the sentence Dogs like to chase cats the verb like is used catenatively; i.e. it is followed by another verb in its infinitive or participial form. If such catenative constructions are passivized they result in extremely questionable utterances such as:
?? To chase cats is liked by dogs. ??Chasing cats is liked by dogs.
I want to go home >> ??To go home is wanted by me.
If a direct object is interposed between the catenative elements such as in:
I helped him to move house
then the passive form is more acceptable but still somewhat questionable:
?He was helped by me to move house.
Similar passivized constructions that do not state the agent are not a problem:
He was permitted to leave early.
She was asked to work on Saturday.
It can be done if you accept turning the verb chase into a gerund:
The chasing of cats is liked by dogs.
The meaning is essentially the same and the resulting sentence is grammatical.
You could also leave the verb as it is:
Chasing cats is liked by dogs.
However, because of the idiomatic nature of language, this can be read as if chasing is used attributively—as if there were such as thing as chasing cats just as there are Siamese cats. If so interpreted, not only do we know there is no such thing but it leads to subject-verb disagreement. So, the use of the gerund leads to better comprehension.
Here, chasing is a gerund: the present participle form of the verb to chase that is being used as a noun.
It has the same grammatical function as:
Eating people is wrong.
Note that while it's also possible to think of eating here as having an attributive function (as with chasing cats), this particular subject doesn't lead to that natural interpretation.
However, the same conversion could still be performed if desired:
The eating of people is wrong.
With the sentence in question, it's the dogs who are the agent of the action of liking. But in what some people consider to be a fully passive sentences, no agent is given at all:
The window was broken.
Without specifying the agent of the action, the sentence would simply be written as:
The chasing of cats is liked.