Is it possible to form a triangle in which the three sides are 8, 21, 14 units in length?

Yes it is possible. Each side is less than or equal to the sum of the remaining two. 8 < ( 21 + 14 ) and 21 < ( 8 + 14 ) and 14 < ( 8 + 21 ) 

Is it possible to form a triangle in which the three sides are 20, 14, 12 units in length?

Yes it is possible. Each side is less than or equal to the sum of the remaining two. 20 < ( 14 + 12 ) and 14 < ( 20 + 12 ) and 12 < ( 20 + 14 ) 

Is it possible to form a triangle in which the three sides are 19, 10, 4 units in length?

No. This will violate the Triangular Inequality. In a triangle the length of each side, is less than the sum of the lenghts of the other two. 19 >= ( 10 + 4 ). So these sides don't form a triangle. 

Is it possible to form a triangle in which the three sides are 8, 21, 4 units in length?

No. This will violate the Triangular Inequality. In a triangle the length of each side, is less than the sum of the lenghts of the other two. 21 >= ( 8 + 4 ). So these sides don't form a triangle. 

Is it possible to form a triangle in which the three sides are 9, 10, 1 units in length?

No.This will violate the Triangular Inequality.  In a triangle the length of each side, is less than the sum of the lenghts of the other two. 10 >= ( 9 + 1 ). So these sides don't form a triangle. 

Is it possible to form a triangle in which the three sides are 11, 23, 8 units in length?

No. This will violate the Triangular Inequality. In a triangle the length of each side, is less than the sum of the lenghts of the other two. 23 >= ( 11 + 8 ). So these sides don't form a triangle. 

Is it possible to form a triangle in which the three sides are 19, 13, 10 units in length?

Yes it is possible. Each side is less than or equal to the sum of the remaining two. 19 < ( 13 + 10 ) and 13 < ( 19 + 10 ) and 10 < ( 19 + 13 )

Is it possible to form a triangle in which the three sides are 9, 20, 15 units in length?

Yes it is possible. Each side is less than or equal to the sum of the remaining two. 9 < ( 20 + 15 ) and 20 < ( 9 + 15 ) and 15 < ( 9 + 20 )

Is it possible to form a triangle in which the three sides are 15, 11, 12 units in length?

Yes it is possible. Each side is less than or equal to the sum of the remaining two. 15 < ( 11 + 12 ) and 11 < ( 15 + 12 ) and 12 < ( 15 + 11 )

Is it possible to form a triangle in which the three sides are 20, 25, 15 units in length?

Yes it is possible. Each side is less than or equal to the sum of the remaining two. 20 < ( 25 + 15 ) and 25 < ( 20 + 15 ) and 15 < ( 20 + 25 )

Is it possible to form a triangle in which the three sides are 9, 7, 14 units in length?

Yes it is possible. Each side is less than or equal to the sum of the remaining two. 9 < ( 7 + 14 ) and 7 < ( 9 + 14 ) and 14 < ( 9 + 7 )

Is it possible to form a triangle in which the three sides are 10, 11, 19 units in length?

Yes it is possible. Each side is less than or equal to the sum of the remaining two. 10 < ( 11 + 19 ) and 11 < ( 10 + 19 ) and 19 < ( 10 + 11 )

Is it possible to form a triangle in which the three sides are 7, 22, 7 units in length?

No. This will violate the Triangular Inequality. In a triangle the length of each side, is less than the sum of the lenghts of the other two. 22 >= ( 7 + 7 ). So these sides don't form a triangle. 

Is it possible to form a triangle in which the three sides are 10, 11, 16 units in length?

Yes it is possible. Each side is less than or equal to the sum of the remaining two. 10 < ( 11 + 16 ) and 11 < ( 10 + 16 ) and 16 < ( 10 + 11 )