through 1) raising the red flag with the major investment banks who had dealings with LTCM 2) coordinating involved banks to intervene. Peter Fisher @NY Fed was the first one to realize that the involved banks didn't know the other banks' exposure to LTCM, and the aggregated risks for the whole sector was much bigger than any single bank's realization, therefore the situation called for a concerted effort to avoid "systematic risk".
Fed didn't risk tax payer's money to directly manipulating the market; and Fed didn't and does not have the mandate to do so. HK goverment changed the rule of the game by directly risking tax payer's money in the stock market. Fortunately it worked out for them.