Pushing boulders is a feature that can only be done with HM04 Strength. HM04 is received after you find the Safari Warden's Gold Teeth in the Safari Zone. When you have the Gold Teeth, give it to the Safari Warden and he will reward you with HM04.
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use strength find wardens teeth in safari zone
any pokemon that can learn strength can push aside a big boulder
get hm strehngt
By using the move strength.
one of you Pokemon in your party need to learn strength.