Since a month has four weeks, the tree will increase its height by 2 feet for 4*4=16 weeks after four months of growing.
Since the tree grows at 2 feet per week, after 16 weeks, the tree would have increased its height by 2*16=<<2*16=32>>32 feet.
If the tree is currently 10 feet tall, its height after four months will be 10+32=<<10+32=42>>42 feet.
#### 42