grammar - Verbs taking only second (direct) object?

I know that some verbs only take second object. In essence,

1. 
   

   
   

   I suggest you to pay the tax -- is wrong.

   
   

   
   


2. 
   

   
   

   I suggest you pay the tax -- is correct.

   
   
   

   
   


3. 
   

   
   

   I said something to her -- is correct.

   
   

   
   


4. 
   

   
   

   I said to her something -- is wrong.

   
   
   

   
   

I want to know that, what do you name such verbs ? How can I know more about such verbs ? Where should seek for more verbs similar to suggest and say ?

It really bothers me, especially when I want to construct a sentence. I always have doubt about correctness of the sentence.

Answer

This is a big question: you need to be clear about a few things before we look at the examples. Best make yourself a cup of coffee before you start reading :-).

"Suggest" and "say" are both normal verbs: they both take a subject, they both take an object. The object is what you are suggesting or saying. There are lots of possibilities for things that you can suggest: see here.

One of the ways to specify a suggestion is with a that-clause:

I suggested [that we should update the web site]

This is where it gets confusing: sometimes we leave out the "that":

I suggested [we should update the web site]

If you want to specify a recipient- the person who receives what you are suggesting or saying- you have to use the preposition "to" followed by the a noun or pronoun.

If the suggestion is a noun, it goes next to the verb, with the recipient at the end:

I suggested refinancing to John

If it's more complex we put the recipient first, followed by the object.

I suggested to John [that we should update the web site]

Sometimes the 'to' is omitted: the noun or pronoun on its own is called an indirect object. The indirect object has to go between the verb and the object: here are examples with and without the 'to'.

I gave the file to John - normal

I gave John the file - indirect object

Taking your examples one at a time:

1. 
   

   
   

   I suggest you to pay the tax

   
   

   
   

This is indeed wrong: "to pay the tax" isn't one of the allowed objects for "suggest". If you used "advise" instead, that works, because advise takes the recipient as an object:

I advise you to pay the tax.

2. 
   

   
   

   I suggest you pay the tax

   
   

   
   

This is correct: if we put back in the "that", we get

I suggest that you pay the tax

3. 
   

   
   

   I said something to her

   
   

   
   

This is correct: we have object-to-recipient

4. 
   

   
   

   I said to her something

   
   

   
   

This is wrong, because a simple noun object must come first unless it's an indirect object. If you were to replace "something: with a more complex expression, the word order would be correct:

I said to her that she should just forget him.

I said to her "Just forget him!"

The indirect objects link contains a list of other words that work like this.