The fed actually sells bonds to increase rates. (The fed also has other ways to increase rates). More importantly though, a major reason why raising rates counters inflation is because it lowers aggregate demand in an economy. If rates are higher, people will be less likely to buy things (especially big and expensive things that you usually have to borrow money for like cars and houses). Therefore, the demand for those things falls and the prices of those things fall too (or at least decrease at a slower rate).
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