Weakness of what muscle groups makes the person to walk uphill difficult, hip flexors and knee extensors or hip extensors? In our bonus session Manvi was mentioning that, one should need gluts strength to go uphill/steps and quads strength to downhill. I found this in Sullivan “Going up step-over-step requires good quadriceps strength and a medium to long residual limb. Going down a steep hill again requires good quadriceps strength and prosthetic control but is accomplished by most individuals.” Please clarify. Thanks.

Indeed, to initiate the hip flexion required to advance a limb up a  stair or an incline, the hip flexors have to be strong. Having now placed the foot on the stair above, the referenced limb is now in a position of hip flexion and knee flexion (while the contralateral limb behind is straight in weight bearing/stabilizing mode). To advance the contralateral limb would require the activation of the hip extensors (Gluts) and knee extensors (Quadriceps) of the referenced, flexed limb in order to straighten it and provide the lift necessary to advance the contralateral limb. Therefore, as Manvi points out, in addition to strong quads, stair ascension would be difficult, if not impossible, without strong gluts.

When descending the stairs, the quadriceps of the referenced limb help in extending the knee and also contribute to keeping the knee locked in extension (for balance) while bringing down the contralateral limb.

It should be noted from your question that O’Sullivan is describing prosthetic gait mechanics which sometimes differs from normal gait mechanics. Nevertheless, the breakdown above does not contradict – rather it supports O’Sullivan’s observation that both ascension and descent require strong quadriceps.