Through which work does Milton intend, 'to justify the ways of God to men'?

Option 4 : Paradise Lost

The correct answer is Paradise Lost.

• Paradise Lost is an epic poem in blank verse by 17th-century English poet John Milton. First published in 1667 in ten books, it was revised by Milton himself and re-published in twelve books in 1674. 
• It is considered to be Milton's masterpiece, and it helped solidify his reputation as one of the greatest English poets of all time.
• The subject of the poem is the Christian story of Mankind's expulsion from the Garden of Eden, after Adam and Eve consume the Fruit of the Forbidden Tree of Knowledge on Satan's provocation. 
• In his Invocation to the Muse in Book 1 of his epic poem, Milton writes that he wants to let the general reader know about "Man's First Disobedience, and the Fruit/ Of that Forbidden Tree, whose mortal taste/ Brought Death into the World, and all our woe,/ With loss of Eden." 
• He continues to request the Muses to sing through him so that he may fulfill his mission in life and "assert Eternal Providence, / And justifie the wayes of God to men." 
• Milton wishes to make his readers aware of the unadulterated power of God to punish evil and do good, and his construction of the character of Satan is ample evidence of that.

 Therefore , Option 4 is the correct answer.

•  Paradise Regained was first published in 1671. It is connected by name to his earlier and more famous epic poem Paradise Lost, with which it shares similar theological themes. This poem, however, deals primarily with the temptation of Christ as recounted in the Gospel of Luke. 
• Samson Agonistes is a tragic closet drama by John Milton. It appeared with the publication of Milton's Paradise Regained in 1671. It draws on the story of Samson from the Old Testament; Samson has been captured by the Philistines, had his hair, the container of his strength, cut off and his eyes cut out.  
• Lycidas is a pastoral elegy written by Milton in tribute to his friend Edward King who had recently suffered a tragic death. It was written in 1637 and it first appeared in a 1638 collection of elegies, Justa Edouardo King Naufrago.