Answer:
4 shots
Explanation:
Currently he makes: 6/10 = 60% 
 
Letting x = additional free throws to make 70%, we can apply
 (6 + x) / (10 + x) = 70% 
 Solving for x: 
(6 + x) / (10 + x) = 7/10 
cross multiply: 
60 + 10x = 70 + 7x 
3x = 10 
x = 3 1/3 
 
Since he can not make 1/3 of a shot, the least number of consecutive shots to get to 70% would be 4.