I just saw this:
If a woman in Hong Kong discovers her husband isn’t being faithful, she is legally allowed to kill him but she can use nothing except for her hands.
Is it true?
No, it isn't.
The chapter of the law of Hong Kong regarding murder is 212 OFFENCES AGAINST THE PERSON ORDINANCE.
It doesn't say anything about cheated wife, and the only circumstances which are specifically excused are:
No punishment shall be incurred by any person who kills another by misfortune, or in his own defence, or lawfully in any other manner.
section 212.13, Attempting to administer poison, or shooting, or attempting to shoot or drown, etc., with intent to murder specifically says that strangulation and suffocation, which are probably the easiest ways to kill a person with bare hands, are unlawful:
Any person who-
(a) attempts to administer to, or attempts to cause to be administered to or to be taken by, any person any poison or other destructive thing; or
(b) shoots at any person; or
(c) by drawing a trigger or in any other manner, attempts to discharge any kind of loaded arms at any person; or
(d) attempts to drown, suffocate, or strangle any person,
with intent in any of such cases to commit murder, shall, whether any bodily injury is effected or not, be guilty of an offence triable upon indictment, and shall be liable to imprisonment for life.
And section 212.14, Attempting to commit murder by means not specified covers every type of murder means and methods by saying:
Any person who, by any means other than those specified in any of the preceding sections, attempts to commit murder shall be guilty of an offence triable upon indictment, and shall be liable to imprisonment for life.
None of them mention anything about such a case. It's reasonable to expect a law regarding allowing a cheated wife to kill her husband, to appear in either the Family Law or the Murder and Violence chapters of the law book. And such a law or case doesn't appear there.
Also, one must remember that the HK law is based on the British law, which doesn't and never did permit such an act.
It's possible that like other cases, a court ruling was misinterpreted by the media, creating a false myth which continues to live on-line through "shocking facts" sites, none of them giving a source for their claim. Moreover, the source cited by the site appearing in the question says that:
Her federation is demanding new rules to plug loopholes in the country's outdated marriage law that allows cheating spouses the freedom to have affairs without risking punishment in the courts. In response the Guangdong provincial government has announced that local courts will allow women, including residents of Hong Kong, whose husbands have taken second wives, to sue the other woman for compensation.
Under the new laws, any man found to be living with a woman who is not his legal wife could be sentenced to two years in a labour camp. The laws would also allow a woman whose husband has formed a second relationship to claim half of all the property he has given to the other wife, even if it is held in the other woman's name. In doing so the courts ruled that the purchase of items such as houses, cars and other gifts for a mistress or a prostitute is in violation of the marital relationship.
Citing the current status of the law regarding adultery without mentioning anything about murder.
Under the current circumstances, where no such law appears in the law book under the Family Law and Bodily Harm sections, and none of the sites claiming the claim cite sources, a reasonable conclusion is that this is simply not true.