The correct answer would be D. Invigorated.
According to dictionary definitions, the verb to instigate means to bring about or to initiate an action or an event, to encourage someone to do something. Some synonyms for this verb are: to incite, to encourage, to provoke, to stimulate and to induce. This information was taken from Google researches.
The option invigorated is the one that better expresses the meaning of instigated in the sentence given, because the verb to invigorate means to give strength or energy to something, to stimulate an action or event. This information was also taken from Google researches.
The answer A. Forced couldn't be correct, because the verb to force means to obligate someone into taking an action or causing an event. According to the context given, the crowd marching across the lawn took this approach without a sign of being forced to do it.
The answer B. Caused couldn't be the correct answer, because the verb to cause means simply to make something (typically bad) happen. According to the context given, there would have to be a bigger influence on the crowd to provoke the approach taken, like a direct influence.
The answer C. Tempted couldn't be the correct answer, because the verb to tempt means to entice or attempt to entice someone to take actions they find attractive but know to be wrong. According to the context presented, it isn't possible to identify such a corruption or attempt to corrupt someone's first choice or ideal, but simply an encouragement to take the approach given.