Just like Mahatma Gandhi, who advocated non-violent methods of struggle, Picasso struggled against fascism [by] peaceful means, namely with his art.

advocated 是动词 advocate 的过去式，advocate 由前缀 ad-（表示"朝向"）和词根 voc（表示"声音、呼喊"）加上后缀 -ate 组成，字面意思是"向...呼喊"，引申为"提倡、主张"。 by 是介词，在这里表示"通过...方式"或"借助...手段"，引出实现目的的方法或途径。