My 24 speed bicycle - Shimano Mercier Galaxy - is
The most probable explanation is that your front derailluer (FD) cable is too tight. You can loosen it one of two ways. First, look to see if the cable passes through any adjuster barrels. These are typically found on the shifter where the cable exits, or else on the downtube near the junction with the headtube. If you find one, turn it clockwise to release tension from the cable. Alternate between checking the shifting (large to middle chainring) and adjusting a quarter turn at a time. If you don't have any adjuster barrels to work with, or if the ones you have are already screwed in all the way, undo the cable anchor bolt on the FD, let a little bit of slack through, and re-tighten it. If you find that the derailler will shift down after you do this, but won't readily shift back up, then you've loosened the cable too much and you need to add more tension either by turning the adjuster barrels counter-clockwise or by pulling the cable taught through the anchor bolt.
If you can't seem to strike a happy balance between upshifting and downshiting, or if you are having trouble shifting in both directions, check to make sure that the FD is positioned correctly. Shift to the middle chainring so you can get a good look at the outer plate of the FD cage relative to the large chainring. Looking from above, the outer plate should be parallel to the large chainring, or else angled inward very, very slightly towards the rear. Looking from the right side of the bike, you should be able to see a 2mm gap between the top of the teeth of the large chainring and the bottom of the plate of the FD.
If the FD is positioned properly, and you can't seem to fix the problem by adjusting the cable tension, check to make sure that the cable is running freely through the housing. To do this, undo the cable anchor bolt and try pulling the cable back and forth through the housing as well as running the housing up and down the length of the cable. The interface between the cable and the housing should be nearly frictionless. While you do this, make sure that the chewed-up part of the cable where the anchor bolt pinches doesn't enter the housing, or else you won't be able to get a good feel. If the cable has trouble moving freely through the housing, pull it out of the housing and wipe it off--if it is kinked or if it rusty in the sections that run within the housing, replace it. If the cable is ok, squirt some oil in the housing, put the cable back in, and test again to see if the cable runs smoothly. If it still doesn't, replace the housing.