gerund and infinitive

Hi,

On the ccc.comnet.edy website, in its section of "GERUNDS AND INFINITIVES: THEIR NOUN ROLES," I am copying as pasting this part:

The verbs in the next table will often be followed by an infinitive, but they will also be accompanied by a second object. We asked the intruders to leave quietly. They taught the children to swim. The teacher convinced his students to try harder.

The verbs in blue, with an asterisk, can also follow the same pattern as the verbs in the table above (i.e., the second object is optional). We all wanted to go. They promised to be home early.

Communication advise ask* beg* challenge command convince forbid invite order permit persuade promise* remind require tell warn urge Instruction encourage help instruct teach train Causing allow cause choose force get hire need* would like* Miscellaneous dare* expect* trust prepare* want* What do they mean by "The verbs in the next table will often be followed by an infinitive, but they will also be accompanied by a second object"? What is the highlighted part? Grammatical term? We asked the intruders to leave quietly I SAW SOME WHERE THAT AFTER CERTAIN VERBS LIKE "SAW THERE IS NO WORD "TO". IS THAT RIGHT? WHAT IS THE PART UNDERLINED? GRAMMATICAL TERM? I saw him drink the water.