"Suggest to go" vs. "suggest going"

I never find much difference in use of infinitive and gerund. However, it is always suggested that few verbs are always followed by gerund whereas few are followed by infinitives only.

I found a good distinction somewhere over the Internet which may help

Gerund

Often we use the gerund for an action that happens before or at the same time as the action of the main verb.

1. I enjoy playing (I enjoy myself at the time of playing.)
2. I denied stealing (I deny having stolen anything before.)

Infinitive
Often we use the infinitive for actions that follow the action of the main verb.

1. I decided to visit my uncle (Visiting my uncle was an action of my decision. It comes after.)
2. I want to go out. (What I want (now) is to go out (after/later))

In your example:

Someone suggested going for a walk.

He suggested for a walk at the same time to be happened not sometime in future.

However someone may suggest for future action too;

Someone suggested to meet Ms Rekha before leaving the Mumbai.

So I personally don't consider that sentence as wrong sentence until the context is given. I found a good explanation for above situation here;

A suggestion (what is suggested, the object of the verb suggest) is a noun. You can't use an infinitive verb where a noun is required.

Going here is a gerund, a form of the verb go which functions as a noun.

[Note that suggested can followed by that and a finite verb, "suggested that we go". That's different; that is a conjunction introducing a clause expressing purpose, end, aim, or desire.]

You wrote in your test "Someone suggested to go for a walk" assuming that to suggest is followed by a to-infinitive as hundreds of other verbs. But to suggest is one of the few verbs that need a gerund, just as to avoid.

There is no logic reason for the gerund construction, it is just a convention and must be learnt (grammar point: verbs + gerund instead of to-infinitive).