Answer:
         Cu  +  4 HNO₃   →   Cu(NO₃)₂  +  2 NO₂  +  2 H₂O
Explanation:
Step 1: Write down the chemical formulas of given substances,
                  Copper Metal  =  Cu
                  Nitric Acid  =  HNO₃
                  Copper (II) Nitrate  =  Cu(NO₃)₂
                  Nitrogen Dioxide  =  NO₂
                  Water  =  H₂O
Step 2: Write down the unbalance Chemical equation,
             Cu  +  HNO₃   →   Cu(NO₃)₂  +  NO₂  +  H₂O
Step 3: Balance Cu atoms on both sides;
The number of Cu atoms on both sides are same. Hence, there number will remain the same.
Step 4: Balance N atoms on both sides;
As there is 1 N atom on left hand side and 3 N atoms on right hand side, so we will multiply HNO₃ by 3 to balance N on both sides, hence,
             Cu  +  3 HNO₃   →   Cu(NO₃)₂  +  NO₂  +  H₂O
Step 5: Balance O atoms on both sides;
As there are 9 O atom on left hand side and 9 O atoms on right hand side, so they are balance.
Step 6: Balance H atoms on both sides;
As there are 3 H atom on left hand side and 2 H atoms on right hand side, so we will multiply Hâ‚‚O by 2 as,
             Cu  +  3 HNO₃   →   Cu(NO₃)₂  +  NO₂  +  2 H₂O
By doing so the number of O atoms got imbalanced, so to balance O atoms again we will multiply HNO₃ by 4 as,
             Cu  +  4 HNO₃   →   Cu(NO₃)₂  +  NO₂  +  2 H₂O
Now, The Cu and H atoms are balanced, and the O atoms are greater on left hand side and the N atoms are greater on right hand side, therefore we will multiply NOâ‚‚ by 2 to balance both N and O as,
             Cu  +  4 HNO₃   →   Cu(NO₃)₂  +  2 NO₂  +  2 H₂O
