I would use a combination of expandRows from my "splitstackshape" package and melt from "reshape2".
Assuming your data are called "mydf", try:
library(splitstackshape)
library(reshape2)
dfLong <- expandRows(
  melt(mydf, measure.vars = c("Yes", "No"), 
       variable.name = "answer"), "value")
Here are the first 20 rows:
head(dfLong, 20)
#        age  color place answer
# 1    12-18    red right    Yes
# 1.1  12-18    red right    Yes
# 1.2  12-18    red right    Yes
# 1.3  12-18    red right    Yes
# 1.4  12-18    red right    Yes
# 1.5  12-18    red right    Yes
# 1.6  12-18    red right    Yes
# 1.7  12-18    red right    Yes
# 1.8  12-18    red right    Yes
# 1.9  12-18    red right    Yes
# 1.10 12-18    red right    Yes
# 1.11 12-18    red right    Yes
# 2    19-30 yellow  left    Yes
# 2.1  19-30 yellow  left    Yes
# 3    12-18    red right     No
# 3.1  12-18    red right     No
# 3.2  12-18    red right     No
# 3.3  12-18    red right     No
# 3.4  12-18    red right     No
# 4    19-30 yellow  left     No
## Confirm that there are the correct number of combinations
table(dfLong$age, dfLong$answer)
#        
#         Yes No
#   12-18  12  5
#   19-30   2 33
The order is a little bit different from what you've posted--doing all "Yes" answers first and then the "No" answers instead of alternating between them.