What does it mean when there are 2 verbs next to each other in a sentence?
1. V1+V2
Chinese permits placing verbs immediately next to one another. In fact this is observed when there are more than two verbs, especially if some of them are auxiliary in nature (e.g. 去, 來).

(1.1) 去 幫忙 做 家務 吧。 Go help do chores.
(1.2) 我 答應 來 幫忙 做 家務。 I promised to come help do chores.

are all grammatical.
2. V+着 as a verb
Only some verbs can have 着 added after them, as 着 suggests a continuous action. So in

(2.1a) *我喜歡着說話。 *I am liking to speak.
(2.2a) *我喜歡說着話。 *I like to be speaking.
(2.3) 我喜歡說話。 I like to speak.

sentences (2.1a) and (2.2a) sound weird, even in English. In a way the continuous tense is unnecessary when indicating general likings and interests. However, that is not to say 喜歡着 and 說着話 are ungrammatical. Using them really depends on the context:

(2.1b) 我一直喜歡着你。 I have always liked you.
(2.2b) 他邊說着話，邊跳着舞。 He is speaking as he is dancing.

We can appreciate the speaker in sentence (2.1b) has liked the listener for quite some time already, from the past all the way to the present. And in sentence (2.2b), both actions are occurring continuously and simultaneously.
3. V+着 as an adverb
In the example

(3.1) 她喜歡站着吃飯。 She likes to eat while standing

站着 can be seen, in a way, as adverbial on the verb 吃, specifying the way she eats. The continuous tense is used because all the while she ate, she was standing. Other examples include

(3.2) 先放着不管那件事。 As of now, leave that matter alone and let it be.

It is hard to translate sentence (3.2) literally into English, but similarly, the verb 放 'to place', together with 着, functions as if it is adverbial on the verb 不管 'to not care', meaning 'to not care about it while placing it there'.
4. On 忘

(4.1) 我忘說了。
(4.2) 我忘記說了。
(4.3) 我忘了說。

There is some awkwardness in sentence (4.1), but it is not ungrammatical (meaning the rule V1+V2 still stands). A better way to phrase it would be using the compound verb 忘記, as shown in sentence (4.2). The awkwardness exists perhaps because 忘 is, in a sense, akin to classical Chinese. Sentence (4.3) is less awkward than (4.1) because 忘 is not used alone, but together with the suffix 了. Other similar compounding include: 忘掉 and 忘卻.