I think this is quite difficult to explain without being there in the flesh, but we'll have a go.
Carbon likes to bond with 4 things, in the case of single bonds. In the case of your structure from left to right it is bonding to 3, 5, 3 and 3 (assuming single bonds). The "carbon atom alone" is bonded to two methyl groups, an ethyl group and the OH group, there is no more to share out and bond to a hydrogen.
3-ethylhexane would have a total of 18 hydrogens, but let's take a step back - where have you got the 14 figure from?