Is 马克又会汉语又会日语 an error in my Chinese book? Isn't 会汉语 incorrect?
会 here is a verb meaning to know.
Here are two sample sentences from A Chinese-English Dictionary:

他还会两出京戏。
Tā hái huì liǎng chū Jīngxì.
He knows a few airs of Beijing opera.



我会英语, 不会日语。
Wǒ huì Yīngyǔ, bù huì Rìyǔ.
I know English but not Japanese.

ABC dictionary defines it as to understand or to grasp

你会吗?
Nǐ huì ma?
Do you know how?